FRLG doesn't really have any HM slaves that are useful for the entire game like RSE Marill or DPPt Bibarel. All the Pokemon that learn a lot of HMs are either obtainable later in the game (like Lapras or Lickitung), require evolution (like Nidoqueen or Dragonite), or are Bulbasaur and Squirtle (which you probably don't want to use as HM slaves).
The best early-game HM slave is probably Farfetch'd, which doesn't require any HMs to obtain and learns both cut and fly. You can replace it with an Aerodactyl or Zapdos later if you want something that learns more HMs along with fly. The best mid-game and late-game HM slave is probably Psyduck, which learns every HM except cut and fly. It's unfortunately FR exclusive, so LG players will need to use a different Pokemon like Poliwhirl, Gyarados, or Lapras.
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