Flotetuzumab for the Treatment of Pediatric Recurrent or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Patients must weigh \>/= 17 kg * Weight limit is due to constraints related to the concentration of the current drug formulation. If a new formulation of flotetuzumab becomes available to allow dosing of smaller patients, the protocol will be amended. * Patients with recurrent or refractory AML are eligible. Patients must have histologic verification of malignancy at relapse. * Patients with leukemia must have \>/= M2 marrow by morphology and/or flow cytometry and one of the following: * Second or greater relapse * Refractory after 2 or more chemotherapy cycles * First relapse after primary chemotherapy-refractory disease * First relapse after hematopoietic stem cell transplantation (HSCT) * Central nervous system (CNS) disease: * Patients must have the status of CNS1 and no clinical signs or neurologic symptoms suggestive of CNS leukemia, such as cranial palsy. * Patients with CNS3 or CNS2 status may receive antecedent intrathecal chemotherapy to achieve CNS1 status prior to study entry. * Patients with a history of CNS chloromatous disease are required to have no radiographic evidence of disease prior to enrollment. * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life. * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1, or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients =/\< 16 years of age. Use appropriate score for study population. NOTE: Patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment. If after the required timeframe, the numerical eligibility criteria are met, e.g., blood count criteria, the patient is considered to have recovered adequately. * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive. * \>/= 14 days must have elapsed after the completion of other cytotoxic therapy with the exception of hydroxyurea. Additionally, patients must have fully recovered from all acute toxic effects of prior therapy. * NOTE: Cytoreduction with hydroxyurea is recommended to be discontinued \>/= 24 hours prior to the start of protocol therapy. No waiting period is required for patients having received intrathecal cytarabine, methotrexate, and/or hydrocortisone. * Anti-cancer agents not known to be myelosuppressive (e.g., not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): \>/= 7 days after the last dose of agent. * Antibodies: \>/= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =/\< 1. * Corticosteroids: If used to modify immune adverse events related to prior therapy, \>/= 14 days must have elapsed since last dose of corticosteroid. * Hematopoietic growth factors: \>/= 14 days after the last dose of a long-acting growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor. For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur. The duration of this interval must be discussed with the study chair and the study-assigned research coordinator. * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>/= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors). * Stem cell infusions (with or without total body irradiation \[TBI\]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or stem cell boost: \>/= 84 days after infusion and no evidence of graft versus host disease (GVHD) * Donor leukocyte infusion: \>/= 42 days * Autologous stem cell infusion including boost infusion: \>/= 42 days * Cellular therapy: \>/= 42 days after the completion of any type of cellular therapy (e.g. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.) * Radiation therapy (XRT)/external beam irradiation including protons: \>/= 14 days after local XRT; \>/= 84 days after TBI, craniospinal XRT or if radiation to \>/= 50% of the pelvis; \>/= 42 days if other substantial bone marrow (BM) radiation * Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131I-MIBG): \>/= 42 days after systemically administered radiopharmaceutical therapy * Patients must not have received prior exposure to flotetuzumab. * Platelet count \>/= 20,000/mm\^3 (may receive platelet transfusions) * These patients must not be known to be refractory to red cell or platelet transfusion * Hemoglobin \>/= 8.0 g/dL at baseline (may receive red blood cell \[RBC\] transfusions) * These patients must not be known to be refractory to red cell or platelet transfusion. * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>/= 70 ml/min/1.73 m\^2 or * A serum creatinine based on age/gender as follows: * Age: Maximum serum creatinine (mg/dL) * 1 to \< 2 years: male - 0.6; female - 0.6 * 2 to \< 6 years: male - 0.8; female - 0.8 * 6 to \< 10 years: male - 1; female - 1 * 10 to \< 13 years: male - 1.2; female - 1.2 * 13 to \< 16 years: male - 1.5; female - 1.4 * \>/= 16 years: male - 1.7; female - 1.4 * Bilirubin (sum of conjugated + unconjugated) =/\< 1.5 x upper limit of normal (ULN) for age regardless of baseline * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =/\< 3 x ULN. For the purpose of this study, the ULN for SGPT is 45 U/L regardless of baseline. * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST/\< 3 x ULN. For the purpose of this study, the ULN for SGPT is 50 U/L regardless of baseline. * Serum albumin \>/= 2 g/dL * Shortening fraction of \>/= 27% by echocardiogram, or * Ejection fraction of \>/= 50% by gated radionuclide study * Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled * Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 5) resulting from prior therapy must be =/\< grade 2 with the exception of decreased tendon reflex (DTR). Any grade of DTR is eligible. * All patients and/or their parents or legally authorized representatives must sign a written informed consent. Assent, when appropriate, will be obtained according to institutional guidelines. * Permanent central access should be established with a central line. A central line that contains 2 lumens is preferred. Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study because there is yet no available information regarding human fetal or teratogenic toxicities. Pregnancy tests must be obtained in girls who are post-menarchal. Males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method for the duration of study therapy and for 12 weeks after flotetuzumab discontinuation. * Patients must be off steroids (unless physiologic replacement dosing) for at least 7 days prior to enrollment. If used to modify immune adverse events related to prior therapy, \>/= 14 days must have elapsed since last dose of corticosteroid. * Patients who are currently receiving another investigational drug are not eligible. * Patients who are currently receiving other anti-cancer agents are not eligible (except hydroxyurea, which may be continued until 24 hours prior to start of protocol therapy). * Patients who are receiving cyclosporine, tacrolimus or other agents to treat graft-versus-host disease post bone marrow transplant are not eligible for this trial. * Patient has French-American-British classification (FAB) type M3 leukemia (acute promyelocytic leukemia) or identification of t(15;17). * Patient has isolated CNS involvement or isolated extramedullary relapse. * Patient with known human immunodeficiency virus (HIV) infection are eligible if he or she has a negative HIV serology and an undetectable viral load. * Patient known to have one of the following concomitant genetic syndromes: Bloom syndrome, ataxia-telangiectasia, Fanconi anemia, Kostmann syndrome, Shwachman-Diamond syndrome or any other known bone marrow failure syndrome. Patients with Down syndrome are eligible for the study. * Patients must not weigh \< 17 kg. * Patients must not have received prior therapy with a CD123 directed antibody or CD123 directed chimeric antigen receptor (CAR) T cells. * Patients who have an uncontrolled infection are not eligible. * Patients who have received a prior solid organ transplantation are not eligible. * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible. * Known hypersensitivity to murine, yeast, or recombinant proteins; polysorbate 80; recombinant human serum albumin; benzyl alcohol; or any excipient contained in the flotetuzumab drug formulation. Additionally, those patients who have had a hypersensitivity reaction to etoposide that is considered likely related to polysorbate 80 are not eligible. * Patients must refrain from driving a motor vehicle or operating heavy machinery while receiving flotetuzumab and for 30 days from the date of last study drug administration.