Instructions
Capture at least 10 wild Pokemon by throwing Poke Balls at them in battle. If you're having trouble catching Pokemon, reduce their HP as much as possible before throwing a Poke Ball. Inflicting status damage, like freezing, sleep or paralysis, also helps.
Go to Vermillion City and walk east. The path becomes Route 11. Continue walking until you reach Diglett Cave. Enter the cave.
Walk through the tunnel and go through the exit to reach Route 2. Walk south and enter the first building you see.
Speak to the man inside. This is an aide of the Pokemon Professor. He checks to see how many Pokemon you've captured. If you have more than 10, you are given HM 05, Flash.
Teach Flash to any Pokemon you desire to use it in the field and in battle. Many Pokemon are able to learn Flash, especially electric-type Pokemon.