If you don’t have Cut, you can get it from the captain of the S. S. Anne, which is docked at Vermillion City. You’ll need a ticket to get onboard, which you get by helping Bill. Cut is required to reach the Vermillion City Gym.
Fly will take up one of the Pokémon’s move slots, so make sure you choose a Pokémon that has a move you don’t need anymore. In order to use Fly, you’ll need to have that Pokémon with you. Try to teach Fly to a useful Pokémon that you’ll have with you often.
You cannot use Fly to visit places you have not yet reached on your journey.