What percentage of money does prison keep if inmate owes a fine?

It depends on what the fine is for. If it is a court fine or a restitution the money goes to that department or entity. The prison is not for profit and any money they receive has an obligation to marshal assets for the government when it is owed by someone in their custody. Even the money that the commissary takes in, if there is a "profit" it is rolled into inmate programs and inmate recreation costs.