Someone says my dog busted out the gate and bit their dogs, but I have no pictures or witnesses

Not sure what the question is. That said - legal liability does not require pictures or witnesses though that is helpful. Either your dog "busted out the gate" or it didn't and it bit other dogs or it didn't. This all revolves aound the type of dog, its history of "bustin out the gate", the type of fencing and gate and its condition, etc. I would start with getting as much detail as possible about the allegations and if the other person is making a claim or demanding damages, you will likely need to retain a lawyer and report it to your homeowners coverage.