Inclusion Criteria:  Refractory AML without CR after induction therapy (primary induction failure); relapsed AML after obtaining a CR; progressive AML after non-intensive therapy (e.g., HMA + venetoclax or targeted therapy); Intermediate risk to very-high-risk MDS by IPSS-R that is relapsed or refractory after prior therapy with an HMA-containing regimen At least 18 years of age.  Available allogeneic donor that meets the following criteria:  Able and willing to undergo multiple rounds of leukapheresis At least 18 years of age In general good health, and medically able to tolerate leukapheresis required for harvesting the NK cells for this study. Negative for hepatitis, HTLV, and HIV on donor viral screen Not pregnant Voluntary written consent to participate in this study All HLA-match/mismatch statuses will be included, with preference for unmatched donors all else being equal Patients with known CNS involvement with AML are eligible provided that they have been treated and CSF is clear for at least 2 weeks prior to enrollment into the study. CNS therapy (chemotherapy or radiation) should continue as medically indicated during the study treatment. Karnofsky/Lansky performance status > 50 %  Adequate organ function as defined below:  Total bilirubin < 2 mg/dL AST(SGOT)/ALT(SGPT) < 3.0 x ULN Creatinine within normal institutional limits OR creatinine clearance ≥ 40 mL/min by Cockcroft-Gault Formula Oxygen saturation ≥90% on room air Ejection fraction ≥35% Able to be off corticosteroids and any other immune suppressive medications beginning on Day -3 and continuing until 30 days after the last infusion of the NK cell product. However, use of low-level corticosteroids is permitted if deemed medically necessary. Low-level corticosteroid use is defined as 10mg or less of prednisone (or equivalent for other steroids) per day. Women of childbearing potential must have a negative pregnancy test within 28 days prior to study registration. Female and male patients (along with their female partners) must agree to use two forms of acceptable contraception, including one barrier method, during participation in the study and until 30 days after the last NK cell product infusion. Ability to understand and willingness to sign an IRB approved written informed consent document  Exclusion Criteria:  Relapsed after allogeneic transplantation. Circulating blast count >30,000/µL by morphology or flow cytometry (cytoreductive therapies including leukapheresis or hydroxyurea are allowed). Uncontrolled bacterial or viral infections, or known HIV, Hepatitis B or C infection. Uncontrolled angina, severe uncontrolled ventricular arrhythmias, or EKG suggestive of acute ischemia or active conduction system abnormalities. New progressive pulmonary infiltrates on screening chest x-ray or chest CT scan that have not been evaluated with bronchoscopy. Infiltrates attributed to infection must be stable/ improving after 1 week of appropriate therapy (4 weeks for presumed or proven fungal infections). Known hypersensitivity to one or more of the study agents. Received any investigational drugs within the 14 days prior to the first dose of fludarabine. Pregnant and/or breastfeeding. Any condition that, in the opinion of the investigator, would prevent the participant from consenting to or participating in the study