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So while doing some orb grinding, I went ahead and test out Flannery's formula. For Ember, this is how the formula will be when critical and burn are met
1.5 [Critical] * Ember damage * (1 [Base] + Burn Synergy + Critical Strike)
However, for the sync move
1.5 [Critical] * 2 (Burn) * Sync Move * (1 [Base] + Critical Strike)
The burn bonus from Sync Move applies differently than Burn Synergy mostly because it's an innate effect from the move itself instead of an addition like Burn Synergy. Below is the comparison of the damage chart of a gridded 3-star Flannery compared to 3-star Erika