Normally named drivers (additional drivers) on the car insurance policy do not earn no claims bonus (NCB); only the main driver/policyholder earns NCB. Therefore if you have an accident, nothing will happen to your dad's no claims because he doesn't have any to start off with on that particular insurance policy of yours. In the event that your dad has another car insurance policy in his name, he would still not lose his NCB if you have an accident as it's a completely different policy and it wasn't him who had the accident (note that we're assuming here that the accident was your fault; if it wasn't your fault, then you wouldn't need to worry about no claims because you won't lose any).
Earlier I said normally named drivers do not earn no claims, this is true for most cases. The exception is that some insurers allow named drivers to earn a separate no claims nowadays but this is only valid with the same insurer, that is, if they change insurance company, it wouldn't be valid anymore.
