Pugno D. Brace deals only 5d6 fire damage per unarmed strike, the rest of the damage is physical, so he is still doing 6d8 damage (2d10 for the unarmed strike damage of a monk of level 18 for VMC monk plus 4 levels for the robes of the monk, this increased by two sizes for Kinetic Form) + 19 (dexterity plus weapon enhancement plus 1 damage for having chosen Fire twice for Expanded Element). When using pummeling charge he can make his flurry, for a total of 6 six attacks, with two extra attacks thanks to haste and using a KI point, resulting in:
6d8 (average, 27) + 19 = 46 damage per attack
46 * 8 attacks - 15 DR (applied only once, thx to Pummeling Style) = 353 total damage.
The Balor is down on his next turn (retreat is not an option in this challenge), while the balor does not have any real option to do anything (per the post).
Same goes for the Pit Fiend (which may fail the ST against blindness of the Flashing Infusion) and the Goldie (here Pugno D. Brace has the edge because he gets the surprise round and then wins initiative).