A friend and I were jousting targ and lanni today, and targ played Flame-Kissed (core) on Myrcella Lannister (LotR). Can she be discarded as a response and put into discard rather than killed?

No. For one thing, her ability is not a Response. So she cannot be discarded in "response" to anything.

There are no "last in, first out" chains in this game. Each effect that is initiated must resolve completely before the next one can be initiated. The only effects that can interrupt the "initiation-resolution" chain of another effect are "Response" effects that use the word "save" or "cancel." Myrcella's "discard for another challenge" effect doesn't fit.

Perfect, thanks!