So I'm assuming the second of the following two examples is the one that happens?
Turn 1: My Scizor with Rejuvenate uses Bullet Punch on a Chandelure. Chandelure uses Flamethrower on Scizor. Scizor faints, then rejuvenates. Turn ends.
Turn 2: My Scizor uses Bullet Punch again, since the turn in which my Scizor couldn't move already ended.
Turn 1: My Scizor with Rejuvenate uses Bullet Punch on a Chandelure. Chandelure uses Flamethrower on Scizor. Scizor faints, then rejuvenates. Turn ends.
Turn 2: I select Bullet Punch for Scizor again, but it can't be executed, since it was rejuvenated last turn. Chandelure uses Flamethrower. Scizor faints, then rejuvenates. Turn ends.
Turn 3: I select U-Turn for Scizor, but it can't be executed, since it was rejuvenated last turn. Chandelure uses Flamethrower. Scizor faints, then rejuvenates. Turn ends.
Turn 4: I select Slash for Scizor, but it can't be activated, since it was rejuvenated last turn. Chandelure uses Flamethrower. Scizor faints, then rejuvenates. Turn ends.
...and so on.
If it's the second scenario that happens, keep in mind that obviously a Pokémon with Rejuvenate can infinitely stall a Pokémon with only one-hit knockout attacking moves (Choice Band or Choice Specs, etc.)