Most Pokémon Powers shut down when that Pokémon is affected by a Special Condition. Burned is a Special Condition. This is sort of a mass errata issued long, long ago (under WotC). I'll post the announcements, but they were originally made via chat, so there are MANY annoying typos.
* [Effective 1/17/02:] There is alsoa new Pokemon rule change that will even FURTHER give the current environment somediversity. In working on keeping the Pokemon rules as close as possible to the Japaneserules of the game, there is a new term that will be introduced in a later set thisyear. This is "Special Conditions". Asleep, Confusion, Paralysis, POISON,and later on Burned are all defined as Special Conditions. All of these effects areremoved from the Active Pokemon if they Evolve, Devolve, Leave Play, or are Benched.They ALSO shut off ALL Pokemon Powers on the Pokemon effected by a Special Condition.This means that Poison (and later on Burned) shut off Pokemon Powers on the Pokemonaffected by them. This is a clarification of the rules for Pokemon and WILL takeplace in all of the upcoming Challenge series events and tournaments. TPC has toldus that is how it supposed to work. (Jan 17, 2002 WotC Chat Announcements & Q1280)
* Basically any Pokemon Power on any Pokemon that says it stops working if the Pokemonis Paralyzed, Asleep, or Confused, now should ALSO include Poisoned, or Burned aswell. These 5 effects are known as Special Conditions. Almost every Pokemon powerstops working if its Pokemon has a Special Condition on it. If a Pokemon power saysit still functions if Asleep, Conufused, or Paralyzed, that also holds true for Poisonedand Burned as well. Char, while similar to Burned is NOT the same thing and doesNOT fall under this rule change. All Special Conditions are removed from a Pokemonif it Evolves, Devolves, Leaves play, or is Benched. (Jan 17, 2002 WotC Chat, Q1278& Q1284)