Aside from level 1 moves, Nidoking only learns two moves by level-up in FRLG, both of which are pretty good for an ingame moveset: Thrash at level 22 and Megahorn at level 43. However, the best move in Nidorino's learnset, Horn Drill, comes at level 53. This leaves you with several options:
- Evolve it at level 22, getting Nidorino's Horn Attack and NidoKing's Thrash and Megahorn
- Evolve it at level 43, getting Nidorino's Fury Attack and Flatter, and Nidoking's Megahorn
- Evolve it anytime after level 53 for Nidorino's Horn Drill.
If you evolve it after a point where Nidoking learns one of those moves, then you could use the move relearner on One Island to teach it those moves. For this reason, I would recommend waiting for level 53, since the relearner won't be able to teach moves from Nidorino's learnset after it evolves. Although if you don't want Horn Drill, then I recommend evolving it before or at level 22, since Thrash and Megahorn are better than anything Nidorino learns outside of arguably Horn Drill.