UngeheuerLich
Legend
i would say: add a bonus from deadly strike overrides flurry´s "add no bonus".
I think this is one of the positives of doing an open playtest... that already eagle-eyed players are looking at the wording of abilities and what they mean and how they apply. So that WotC can realize what exactly was the intended way of how these things should or shouldn't combine... and can do their editing passes later on to fix these loopholes that will get pointed out.
Is FoB's "no bonuses" meant to be just STR or DEX mod and/or magic item bonus related? Then Deadly Strike perhaps need to be touched up to not call their damage a "bonus" so that it is clear it can apply. But if not... if FoB's damage is strictly the Expertise Die... then perhaps that needs to be made more explicit too.
This kind of continual light hammering on the terminology can only help keep things clearer as the game goes through its many iterations over the next couple years.