Say you're a monk who wears an Amulet of Mighty Fists which makes your unarmed strike Flaming. Say you then take the Elemental Fist feat, and choose to use it to deal fire damage. The text of Elemental Fist reads "...On a successful hit, the attack deals damage normally plus 1d6 points of damage of the chosen type."
In this event, your attack normally deals (assuming you're 11th level) 1d10+Str+1d6 fire. With Elemental Fist, would it be 1d10+Str+2d6 fire? Or would you have to choose a different element, and deal 1d10+Str+1d6 fire+1d6 electric?
I can't find anything saying you cannot use both the AoMF fire damage and the elemental fist fire damage also...seems to work just fine :)
I believe they would stack since the damage is from different sources. However, I would recommend against fire. Acid is the least resisted element by number of monster in the bestiary.