If I have Kingdra with the "Deep Sea King" Ability on the bench and my opponent uses Heatmor's "Burning Licks" attack that discards energy cards from my Active Pokemon and also knocks it out, can I move those energy cards to Kingdra before they are discarded?
No, the discard effect of the attack happens first, but you don't move energy for Deep Sea King until after you resolve the Knock Out.
Burning LicksDeep Sea King