Re-volter damage does not appear to activate for the pet when Fl4k’s shield goes down. (note: I only tested this with the Guard Skag)
Re-volter enrage DOES apply to pet damage if Take This! is taken and pet’s shield drops, activating an instance of enrage on the pet. This also seems to boost reflected damage from He Bites! This boost did not seem to be shared to Fl4k (note: tested only with Guard Skag and Great Horned Skag)
It probably won’t provide any more insight but here’s a picture of a couple skag hits after its shield was depleted.
Extra comments- Unsure about the conditions for enrage to activate. Does the shield need to recharge fully in between enrage procs? I observed it activating twice in a row without a full recharge but that could have mistaken on my part. But if a full recharge is not needed then Better Toys is actually somewhat useful to get some capacity back quicker by dropping the recharge delay (not saying that skills is good though lol) to queue up another potential enrage. I did not check if it boosted Atomic Aroma before getting off though I wanted to. I only had a short window to play so I settled on the basics.