WHATEVER IS BEST FOR YOUR TEAM.
Your Nidoking has nearly perfect coverage with those three moves, able to hit every Pokemon (except Shedinja) unresisted.
Therefore, a status move (such as Toxic) or a support move (such as Stealth Rock) or a gimmicky move ( such as Suckerpunch) would only serve to make him slightly stronger.
Flamethrower (or Fire Blast for added power) would also be a pretty good option, and it would give you perfect coverage.
However, Nido's movepool is pretty diverse. He can learn thunder(bolt), surf, and a slew of other excellent coverage moves. It really depends on your team.
A large percentage of the Pokemon that take neutral damage from your Nidoking's current attacks are Water and Flying types.
Source: PokemonDB's Type coverage checker.
Most flying types are faster than he is, and he will struggle against bulky waters without Thunder(bolt).
I suggest Thunder. It has the necessary power for Nido's decent Special Attack with Life Orb, as well as hitting a good deal of all Pokemon for super effective damage.
Plus, Shedinja isn't seen so much.