ALT-801-activated Natural Killer Cells After FLAG Induction for Acute Myeloid Leukemia

Recipient Inclusion Criteria: 1. Patients with relapsed AML, including those with CNS disease or previous hematopoietic stem cell transplantation, or primary refractory AML (primary AML that has failed remission to at least two cycles of induction therapy) 2. For patients of Cohorts 2 to 4, availability of a haploidentical family peripheral blood stem cell donor selected for best possible KIR reactivity 3. Patient is between 2 and 59 years of age, inclusive 4. Patient must have recovered from the treatment-related toxicities of prior cytotoxic agents received in the 4 weeks prior to beginning treatment on this protocol, with the exception of cytopenias resulting from persistent disease, and alopecia 5. Zubrod performance scale (Refer to Appendix C) ≤ 2 or Lansky (Refer to Appendix D) \> 60 6. Adequate renal function defined as: * For adults serum creatinine \< 2 mg/dL * For children serum creatinine \< 2 mg/dL or \< 2 times upper limit of normal (ULN) for age (which ever is less) If abnormal creatinine level, 24h creatinine clearance \> 60 mL/min/1.73m\^2 7. Adequate liver function, defined as: Total bilirubin ≤ 2 mg/dL and SGPT (ALT) ≤ 2.5 x ULN for age (unless Gilbert's disease or abnormal liver function due to primary disease) 8. Pulmonary symptoms controlled by medication and pulse oximetry\> 92% room air 9. New York Heart Association classification \< III 10. Negative serum test to rule out pregnancy within 2 weeks prior to registration in females of childbearing potential (non childbearing potential defined as premenarchal, greater than one year post-menopausal, or surgically sterilized) 11. Sexually active males and females of childbearing potential must agree to use a form of contraception considered effective and medically acceptable by the Investigator 12. Negative serology for human immunodeficiency virus (HIV) Recipient Exclusion Criteria: 1. Investigational therapies in the 4 weeks prior to beginning treatment on this protocol 2. Congestive heart failure \< 6 months prior to screening 3. Unstable angina pectoris \< 6 months prior to screening 4. Myocardial infarction \< 6 months prior to screening Donor Inclusion Criteria: 1. Related to recipient (sibling, parent, offspring, offspring of a sibling) 2. HLA-haploidentical to recipient (need not be re-tested if already performed previously, provided copies of the original results are available) 3. Able and willing to undergo apheresis 4. Willing to donate blood for baseline chimerism assessment 5. Negative serum test to rule out pregnancy within two weeks prior to registration in females of childbearing potential (non childbearing potential defined as premenarchal, greater than one year post-menopausal, or surgically sterilized) 6. Donor must meet institutional eligibility criteria for allogeneic blood stem cell donation including infectious disease screening panel (Hepatitis B, Hepatitis C, HIV, CMV, and West Nile Virus) and CBC, differential and platelet studies 7. Donor must meet stem cell donor eligibility criteria as set forth in 21 CFR 1271 subpart C 8. The preferred Donor will be selected as the most alloreactive of the available haploidentical related donors on the basis of predicted NK cell alloreactivity using Recipient and Donor HLA type. If necessary, the best of equally alloreactive donors will be determined by Donor KIR type. NK alloreactivity is defined as o A KIR gene is present on the Donor NK cells for which * the HLA haplotype (KIR ligand) for the KIR receptor in question is absent in the Recipient, and * the HLA haplotype (KIR ligand) for the KIR receptor in question is present in the Donor Donor Exclusion Criteria: 1. Active infection (defined as on antimicrobial therapy and/or febrile) 2. Pregnant females 3. Breast-feeding females