• Age ≥ 18 years.

• Individuals with histologically or pathologically confirmed diagnosis of relapsed or refractory AML with documented FLT3 mutation, and/or Individuals with histologically or pathologically confirmed diagnosis of their malignancy with wild-type FLT3 (including those with MLL1-R and NPM1 mutations).

• ECOG performance status of 0-2.

• Adequate liver and renal function

• Adhere to the CYP3A4 inhibitor concomitant therapy use requirements, as follows:

• Arm A: Participants must not have received a moderate or strong CYP3A4 inhibitor for at least 7 days prior to enrollment and are not anticipated to require such agents in the near term (for at least 4 weeks).

• Arm B: Participants must have received a necessary azole antifungal(s) that is a strong CYP3A4 inhibitor (excluding other strong CYP3A4 inhibitor\[s\]) for at least 7 days prior to enrollment and be able to continue such azole antifungal(s) while on BMF-500 treatment for at least 4 weeks.

• Arm C: Participants must have received necessary azole antifungal(s) that are moderate CYP3A4 inhibitors (excluding other moderate CYP3A4 inhibitors) for at least 7 days prior to enrollment and be able to continue such azole antifungal(s) while on BMF-500 treatment for at least 4 weeks (Cycle 1).