I think this might sum it all up:
Bassist Flea, on the music video: "We mainly did eras, not actual people: rockabilly, British Invasion, Psychedelia, Funk, Glam, Punk, Goth, Hair Metal, Grunge, and ourselves being the sum of all those parts."
The bands that the Peppers dress up in during the video caused internet debate about who the actual bands were. Though nothing is official, it starts out in a '50s early Rock setting, with Anthony Kiedis dressed as Elvis Presley. It then moves on to a stereotypical British Rock band that you would see on The Ed Sullivan Show in the '60s. They move on to a stereotypical Psychadelic Rock band, then the Funk era. The band is dressed as Parliamant/Funkadelic, complete with Flea dressed as one of his idols, Bootsy Collins, and the P-Funk Mothership stage prop.
It moves on to a stereotypical Glam Rock band, then Gothic band, most likely The Misfits based on the way Kiedis is dressed. Then it moves on to the Punk movement, Hair Metal, and Grunge. The Grunge band is one of the more clear bands to identify, as Kiedis is dressed like his friend Kurt Cobain, of Nirvana. It ends with the Peppers as a sum up of all of these bands.
https://www.songfacts.com/facts/red-hot-chili-peppers/dani-california
