ΔE 12.8, fair: the same colour family, but not a straight swap. Flesh Wash is a little lighter, more saturated, cooler than Battle Mud Wash.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 13). Flesh Wash is a little lighter, more saturated, cooler than Battle Mud Wash.
The same difference applies the other way round: Battle Mud Wash is a little darker, more muted, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Battle Mud Wash on the colour wheel See Flesh Wash on the colour wheel
All matches: Battle Mud Wash equivalents · Flesh Wash equivalents