From Page 45 of the Rules Manual:
If the Black Joker was flipped for damamge, the model flipping it cannot Cheat Fate and the Damage Flip inflicts no damage.
While you could argue that you'd still get the +1 dg from Critical Strike, the Errata clarifies this with the following:
1. Total the Damage being inflicted.
First, determine the amount damage being inflicted; including performing a Damage Flip if one is required. If the initial Damage Flip is the Black Joker, skip to Step 6 below.
Then, add any applicable damage bonuses.
Then, any Triggers which occur when damage is inflicted occur now.
Finally, reduce the amount of damage being inflicted by the above amount.
6. Any Triggers which occur after resolving damage/wounds occur now.
So since the Black Joker forces you to skip all the way down to step 6 in damage resolution, you skip the activation of any triggers that add damage.