In generation I, II, III, IV (Red, Blue, Green, Yellow, Gold, Silver, Crystal, Fire Red, Leaf Green, Heart Gold, Soul Silver) you obtain the Thunder Badge in Vermillion City. South of Cerulean City.
The Rainbow Badge
* Pewter Gym - Rock Badge * Cerulean Gym - Cascade Badge * Vermillion Gym - Thunder Badge * Celadon Gym - Rainbow Badge * Fuchsia Gym - Soul Badge * Saffron Gym - Marsh Badge * Cinnabar Gym - Volcano Badge * Viridian Gym - Earth Badge
The Thunder Badge
Blue is the Viridian City Gym Leader (Badge #16)
You get the Marsh badge from defeating Sabrina, who is the gym leader in Saffron City. Sabrina uses psychic Pokemon.
the thunder gym in in vermillion city
To get the last gym badge you have to go to cinnabar island and you will meet blue. he will tell you that he will be waiting in veridian city to battle you. when you go to veridian city you go to the gym and fight him at the end of the gym.
you have to get all of the other gym badges in kanto and then go to Cinnabarr island and talk to blue. then go to viridian city and go in the Pokemon gym!
to make fly work, you have to get the thunder badge from Lt.Surge (the gym leader in vermilion city) then get fly.
the seventh gym badge snowpoint gym
Go for the next gym badge.
the fourth gym is in celadon city at the bottom left of the city. the gym leader is erika. the badge is called the rainbow badge