I'm thinking of not paying a fine I received using my brothers car
I am not sure I understand. Will not doing so have any effect on your brother?
It won't affect him at all.
It's good that it won't hurt him, but that doesn't change the fact that you need to take care of it anyways. People need to pay their debts!
Fuck the feds.
It is a bad idea to leave this debt unpaid. Don't you think it will be upsetting to your brother if he one day gets billed for this?