There's a key. You need to go into the mansion on the island, it's in a room in the basement that's difficult to get to... after you get it you can open the door to the gym.
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bottom floor of Pokemon Mansion
Cinnabar Island
You need to acquire the Secret Key that can be found in the basement of the Pokémon Mansion and then you can use the Secret Key to enter into Blaine's Gym.
You explore the mansion until you come to a room with two houseplants. There'll be a pokeball there. Pick it up. It's the key.
The fourth gym at Pokemon fire red is grass type gym