I assume you mean "..and not during your shooting phase" up the top there.A couple things I'm a little unclear on with this power, since it's done at the beginning of the turn and during the shooting phase...
Does the model count as having shot at that target? I.E. if I have a Daemon Prince with Mark of Tzeentch using it twice, do both targets need to be in the same unit, and would he have to assault that unit? Or would it be legal to, say, use Gift on a nearby unit at the beginning of the turn, then fire a Bolt of Change at a tank in the shooting phase, then assault the tank if it's still there?
Also, does it count against your shooting per turn? If not, could, say, a Thousand Sons Sorcerer use Gift of Chaos twice, then shoot his pistol in the shooting phase?
It's only during the beginning of the turn. It isn't a shooting power. It just needs range, nothing else - no LoS, no assaulting the same target, or anything else. With a Tzeenchian caster, you can even cast it twice (or three times with Ahiriman). So what you're proposing (Gift, Move, BoC, Assault) is perfectly legal.
Hope that helps