Alvocidib in Combination With Decitabine and Venetoclax in Patients With Relapsed or Refractory AML or as Frontline Therapy in Unfit Patients With AML

Inclusion Criteria: * Diagnosis of relapsed or refractory acute myeloid leukemia by World Health Organization (WHO) criteria. Unfit/frail patients with newly diagnosed AML are also eligible if not considered good candidates to receive a higher intensity therapy * A patient is considered unfit or frail if has three or more of the five factor below: * Unintentional weight loss of 10 pounds or more in a year * General feeling of exhaustion * Weakness as measured by grip strength * Slow walking speed * Low levels of physical activity * Eastern Cooperative Oncology Group (ECOG) performance status score of =\< 3 * 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 * Alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) =\< 3 x ULN; or =\< 5 x ULN in case of suspected leukemic liver involvement * Serum creatinine =\< 2.0 mg/dl * Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (B-HCG) pregnancy test result within 1 week (+/-3 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 (such as condom used with spermicide or abstinence) 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: * Patients with t(15;17) karyotype abnormality or acute promyelocytic leukemia * 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) \< 45% are excluded * 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 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 tumor burden, leukocytosis (circulating blast count) or palliation: Intravenous cytarabine and/or hydroxyurea. No washout is 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 alvocidib * Prior use of venetoclax single agent or any venetoclax-based combination therapy is allowed