can you play Flame Chompers for 1 power when burned from deck

No. Flame Chompers only triggers "when you discard me," and Burn isn't Discard.

Discard is specifically hand → trash (Rule 423.1), while Burn moves cards from the top of your Main Deck to your trash (Rule 441.1). Burning a card never satisfies a "when you discard me" trigger, so if Flame Chompers is burned off the top of your deck, it just sits in the trash with no ability triggering — you can't pay the fury rune to play it. You'd need a separate recursion effect to get it back.