Alvocidib, Cytarabine, and Mitoxantrone Hydrochloride or Cytarabine and Daunorubicin Hydrochloride in Treating Patients With Newly Diagnosed Acute Myeloid Leukemia

Inclusion Criteria:

* All adults with established, pathologically confirmed diagnoses of newly diagnosed AML and adults with newly diagnosed AML, excluding newly diagnosed core-binding factor (CBF) AMLs and acute progranulocytic leukemia (APL, M3), will be considered eligible for study
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-3

  * Patients \>= 65 years of age must have ECOG PS =\< 2 prior to developing leukemic symptoms
* Serum creatinine ≤ 2.0 mg/dL
* Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< 5 times upper limit of normal (ULN) (unless leukemic infiltration)
* Total bilirubin =\< 2.0 mg/dL (unless Gilbert disease, hemolysis, or leukemia)
* Left ventricular ejection fraction ≥ 45%
* Newly diagnosed AML, subtypes M0, 1, 2, 4-7 but excluding M3 (APL), including those with the following poor risk features:

  * Antecedent hematologic disorder including myelodysplasia (MDS)-related AML (MDS/AML) and prior myeloproliferative disorder (MPD)
  * Treatment-related myeloid neoplasms (t-AML/t-MDS)
  * Myeloid sarcoma, myeloid proliferations related to Down Syndrome, and blastic plasmacytoid dendritic cell neoplasm
  * AML with multilineage dysplasia (AML-MLD)
  * Adverse cytogenetics (defined as -5/-5q; -7/-7q; abnormal 3q, 9q, 11q, 20q, 21q, or 17p; t(6;9); t(9;22); trisomy 8; trisomy 13; trisomy 21; and complex karyotypes (≥ 3 unrelated abnormalities)
* Patients who have received hydroxyurea alone or have received non-cytotoxic therapies previously for myelodysplasia (MDS) or myeloproliferative disorder (MPD) (e.g., thalidomide or lenalidomide, interferon, cytokines, 5-azacytidine or decitabine, histone deacetylase inhibitors, low-dose cyclophosphamide \[cytoxan\], tyrosine kinase \[TK\] or dual TK/src inhibitors) will be eligible for this trial

  * At least 24 hours since prior leukopheresis or hydroxyurea for cytoreduction

Exclusion Criteria:

* Any previous treatment with flavopiridol
* Concomitant chemotherapy, radiation therapy, or immunotherapy
* Hyperleukocytosis with \>= 50,000 blasts/uL; leukopheresis or hydroxyurea may be used immediately prior to study drug administration for cytoreduction; must be stopped 24 hours before first dose of study chemotherapy
* CBF AMLs associated with t(8;21) or M4eo subtype (inv\[16\] or t\[16;16\]), as diagnosed by morphologic criteria, flow cytometric characteristics, and rapid cytogenetics or FISH or molecular testing
* Acute Progranulocytic Leukemia (APL, M3)
* Active central nervous system (CNS) leukemia
* Active, uncontrolled infection; patients with infection under active treatment and controlled with antibiotics are eligible
* Active, uncontrolled graft vs. host disease (GVHD) following allogeneic transplant for non-AML condition (e.g. MDS, lymphoid malignancy, aplastic anemia); patients with GVHD controlled on stable doses of immunosuppressants are eligible
* Presence of other life-threatening illness
* Patients with mental deficits and/or psychiatric history that preclude them form giving informed consent or from following protocol
* Pregnant and nursing patients are excluded