If I have Floral Crown attached to my Active Pokemon, and my opponent does just enough damage to knock it out, can I use Floral Crown to reduce the damage so it is not Knocked Out?

No. You have to resolve all effects and triggered results from the attack first, including Knockouts and taking Prizes. After that, if the Pokemon with Floral Crown is still in play, then you would heal 20 damage. It will not save a Pokemon from a Knock Out due to an attack.

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