Sorafenib Tosylate Before and After Donor Bone Marrow Transplant in Treating Patients With Acute Myeloid Leukemia

Inclusion Criteria: * Acute myeloid leukemia with a FLT3-internal tandem duplication (ITD) who are in a complete remission or partial remission (less than 10% blasts in marrow) as documented by bone marrow biopsy and who plan to undergo a bone marrow transplantation * Patients who have had count recovery (absolute neutrophil count \[ANC\] \> 500,000/mm\^3; non transfused platelet count over 30,000/mm\^3) and are at least 30 days after induction and/or transplantation but no more than 120 days post transplant * Patients may have received any prior therapy deemed necessary for induction of remission except for patients whom have progressed while on sorafenib; patients who have responded to sorafenib previously are eligible for enrollment on the protocol * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than four months * Total bilirubin less than 2 x upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 x institutional upper limit of normal * Creatinine =\< 1.5 x upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels \> 1.5 x upper limit of normal * The effects of sorafenib on the developing human fetus are unknown; for this reason and because tyrosine kinase inhibiting agents are known to be teratogenic, women of child-be…