If I have multiple Infernapes in play, does each of their "Flaming Fighter" Abilities add 6 more damage to my opponent's burned Pokemon in between turns?
No, Infernape's Flaming Fighter ability does not stack. You are simply placing 6 damage counters instead of 2, regardless of how many Infernapes are in play.
Source: Ultra Prism FAQ (2018-01-19), TPCi Rules Team (2018-02-01)