Liposome-encapsulated Daunorubicin-Cytarabine and Gemtuzumab Ozogamicin in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia (AML) or High Risk Myelodysplastic Syndrome

Inclusion Criteria: * Diagnosis of CD33 positive (\>= 3%), relapsed refractory acute myeloid leukemia by World Health Organization (WHO) criteria. Patients with post-hypomethylating agent (post-HMA) failure high-risk myelodysplastic syndrome (MDS), as defined by the presence of \> 10% blasts, are also eligible. * Patients with MDS or chronic myelomonocytic leukemia (CMML) who received hypomethylating agent based-therapy for the MDS or CMML and progress to AML are eligible at the time of diagnosis of AML regardless of any prior therapy for MDS or CMML. The WHO classification will be used for AML. * Eastern Cooperative Oncology Group (ECOG) performance status score of =\< 2. * Total serum bilirubin =\< 2 x upper limit of normal (ULN). Patients with known Gilbert's syndrome may have a total bilirubin up to =\< 3 x ULN. * Serum creatinine =\< 2.0 mg/dl. * Alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) =\< 3 x ULN; =\< 5 x ULN in case of suspected leukemic liver involvement. * Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (b-HCG) pregnancy test result within 14 days prior to the first dose of study drugs and must agree to use one of the following effective contraception methods during the study and for 30 days following the last dose of study drug. Effective methods of birth control include: Birth control pills, shots, implants (placed under the skin by a health care provider) or patches (placed on the skin); intrauterine devices (IUDs); condom or occlusive cap (diaphragm or cervical/vault caps) used with spermicide; abstinence. * Females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation, oophorectomy, and/or hysterectomy. * Males who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 30 days following the last dose of study drug. * Patients or their legally authorized representative must provide written informed consent. Exclusion Criteria: * History of another primary invasive malignancy that has not been definitively treated and in remission. Patients with non-melanoma skin cancers or with carcinomas in situ are eligible regardless of the time from diagnosis (including concomitant diagnoses). * Presence of clinically significant uncontrolled central nervous system (CNS) pathology such as epilepsy, childhood or adult seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, or psychosis. * Evidence of active cerebral/meningeal disease. Patients may have history of CNS leukemic involvement if definitively treated with prior therapy and no evidence of active disease at the time of consent with at least 2 consecutive spinal fluid negative assessments for residual leukemia and negative imaging (imaging required only if previously showing evidence of CNS leukemia not otherwise documented by spinal fluid assessment). * Patients with active unstable angina, concomitant clinically significant active arrhythmias, myocardial infarction within 6 months, or congestive heart failure New York Heart Association class III-IV. Patients with a cardiac ejection fraction (as measured by either multigated acquisition scan \[MUGA\] or echocardiogram) \< 50% are excluded. * Patients with total cumulative doses of non-liposomal daunorubicin, or other anthracycline equivalent, greater than 200 mg/m\^2. * Patients with uncontrolled, active infections (viral, bacterial, or fungal). * Known active hepatitis B or C infection, or known seropositivity for human immunodeficiency virus (HIV). * Patients with liver cirrhosis or other serious active liver disease or with suspected active alcohol abuse. * Allogeneic hematopoietic stem cell transplantation (HSCT) within 6 months before the start of protocol-specified therapy, or with active acute/chronic graft-versus-host disease (GvHD) requiring systemic treatment; or receiving immunosuppression for GvHD prophylaxis within 2 weeks from the start of study therapy. * Prior chemotherapy/radiotherapy/investigational therapy within 2 weeks before the start of study drugs with the following exception: To reduce the circulating blast count or palliation; single dose intravenous cytarabine or hydroxyurea. No washout necessary for these agents. * Patients must have recovered from acute non hematologic toxicity (to =\< grade 1) of all previous therapy prior to enrollment. * Females who are pregnant or lactating. * Male or female subjects of childbearing potential, unwilling to use an approved, effective means of contraception in accordance with institution's standards. * Other severe, uncontrolled acute or chronic medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and/or would make the patient inappropriate for enrollment into this study. * Prior treatment with CPX-351 or gemtuzumab ozogamicin.