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-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; contraception should continue for at least 30 days after the last dose of sorafenib * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 2 weeks except for intrathecal chemotherapy (i.e., methotrexate, cytarabine, or thiotepa) * Patients may not be receiving any other investigational agents * Patients with uncontrolled hypertension (i.e., persistent grade 3 while undergoing treatment) * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib * Patients with active and/or untreated central nervous system (CNS) leukemia will not be eligible * Patients must not have any evidence of bleeding diathesis or be on any therapeutic anticoagulation such as low molecular weight (LMW) heparin or warfarin for deep vein thrombosis (DVT) treatment * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because sorafenib is chemotherapeutic agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with sorafenib, breastfeeding should be discontinued if the mother is treated sorafenib * Human immunodeficiency virus (HIV)-positive patients are excluded because management of these patients in the hematopoietic cell transplant setting has not yet been well defined and is currently the subject of investigation in other studies addressing this issue * Patients with active acute GVHD who have been initiated on therapy or had therapy escalation within 21 days are not eligible * Patients with lack of engraftment (less than 90% donor deoxyribonucleic acid \[DNA\] in bone marrow or peripheral blood) after bone marrow transplant as evidence by RFLP (restriction fragment length polymorphism) are not eligible * Patients who are unable to swallow pills are not eligible * Patients taking strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitors including enzyme-inducing anti-epileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin, grape fruit juice, or St. John's wort are not eligible