Open Label NK Cell Infusion (FATE-NK100) With Subq IL-2 in Adults With AML

Inclusion Criteria: \- ≥18 but ≤ 70 years of age * Diagnosis of acute myeloid leukemia (AML) and meets one of the following disease criteria: \* Primary induction failure: \*\* De Novo AML: no CR after 2, 3 or 4 induction attempts with high dose chemotherapy * Secondary AML (from MDS or treatment related): no CR after 1, 2 or 3 cycles of high dose chemotherapy * Relapsed: * Not in CR after 1 or 2 cycles of standard re-induction therapy * Relapse diagnosed at the time of the 6 months post-HCT standard of care follow-up or later (i.e. based on bone marrow biopsy performed Day +170 or later) and without evidence of graft versus host disease (GVHD) * For patients \> 60 years of age, the minimum of 1 cycle of standard chemotherapy is not required. * Available HLA-matched or better but not fully HLA-matched (2/4 or 3/4 antigens) related donor (aged 18 to 75 years) with donor/recipient match based on a minimum of intermediate resolution DNA based Class I typing of the A and B locus who is CMV seropositive. * Karnofsky Performance Status ≥ 60% * Adequate organ function within 14 days of study registration (28 days for pulmonary and cardiac) defined as: * Creatinine: Estimated glomerular filtration rate (eGFR) ≥ 50 mL/min/1.73m\^2 per current institutional calculation formula * Hepatic: AST and ALT ≤ 3 x upper limit of institutional normal * Pulmonary Function: oxygen saturation ≥ 90% on room air; PFT's required only if symptomatic or prior known impairment - must have pulmonary function \>50% corrected DLCO and FEV1 * Cardiac Function: LVEF ≥ 40% by echocardiography or MUGA * No symptomatic active conduction system abnormalities * Able to be off prednisone or other immunosuppressive medications for at least 3 days prior to FATE-NK100 cell infusion (excluding preparative regimen premedications) * Sexually active females of child bearing potential and males with partners of child bearing potential must agree to use effective contraception during therapy and for 4 months after completion of therapy * Voluntary written consent prior to the performance of any research related procedures Arm Specific Inclusion Criteria High-Risk aGVHD (ARM 1): \- Pediatric or adult (ages 0-76 years) HCT recipients with high-risk acute GVHD, as determined either by the refined MN acute GVHD risk score \[28\]: http://z.umn.edu/MNAcuteGVHDRiskScore OR high risk on the basis of blood biomarkers (Ann Arbor Score 3) \[31\]. Patients in this arm must start treatment within the first 7 days after onset of high-risk aGVHD. or Steroid- Dependent aGVHD (ARM 2A): \- Pediatric or adult (ages 0-76 years) HCT recipient with grade II-IV steroid-dependent acute GVHD, defined as any one of the following: Flare of acute GVHD of at least grade II/IV severity within 8 weeks of tapering down or (off of) immunosuppression for acute GVHD, with the flare occurring on ≤0.5 mg/kg prednisone. This can include late-onset aGVHD and overlap syndrome. or Steroid-Refractory aGVHD (ARM 2B): \- Pediatric or adult (ages 0-76 years) HCT recipient with grade II-IV steroid refractory acute GVHD, defined as any one of the following: * No response of acute GVHD after at least 4 days of systemic corticosteroids of at least 2 mg/kg prednisone or equivalent * Progression of acute GVHD within 3 days of systemic corticosteroids of at least 2 mg/kg prednisone or equivalent * Failure to improve to at least grade II acute GVHD after 14 days of systemic corticosteroids, with initial doses of at least 2 mg/kg prednisone or equivalent * Flare of acute GVHD of at least grade II/IV severity while on steroids at a dose \>0.5/mg/kg/day. This can include late-onset aGVHD and overlap syndrome. Exclusion Criteria: * Myocardial Infraction (MI) within the previous 6 months * Acute leukemias of ambiguous lineage * Pregnant or breastfeeding - The agents used in this study include those that fall under Pregnancy Category D - have known teratogenic potential. Women of child bearing potential must have a negative pregnancy test at screening * History of or known active CNS involvement with AML * Active autoimmune disease requiring systemic immunosuppressive therapy * History of severe asthma and currently on chronic systemic medications (mild asthma requiring inhaled steroids only is eligible) * New or progressive pulmonary infiltrates on screening chest X-ray or chest CT scan unless cleared for study by Pulmonary. Infiltrates attributed to infection must be stable/improving (with associated clinical improvement) after 1 week of appropriate therapy (4 weeks for presumed or documented fungal infections). * Uncontrolled bacterial, fungal or viral infections including HIV-1/2 or active hepatitis C/B - chronic asymptomatic viral hepatitis is allowed * Received any investigational agent within the 14 days before the start of study treatment (1st dose of fludarabine)