The first time I heard about Riot Grrrls was when I met a friend of mine, years ago. We were 17 and she had this insane passion for this kind of music I couldn't barely listen to. It was definitely to noisy for me (I am not for the pop music, but I like a little bit of "melody" you know...). But I went very interested in their look and scene...
Riot Grrrls movement grew up in Washington in the early 90's. They were feminists. Bikini Kill and Bratmobile were the leading groups in the scene. Kathleen Hanna was the Bikini Kill leader. She studied photography at the Evergreen State College in Olympia when she decided to open a small art gallery called "Reko Muse", where artist such us The Go Team used to perform. Meanwhile she started a band with Amy Carter, Heidi Arbogast and Tammy Rae Carland. After a while she hooked up with the drummer Tobi Vail and they started working together on a fanzine called Bikini Kill, which after the advent of Kathi Wilcox and Billy "Boredom" Karren, became a band.
Bratmobile's leader was Allison Wolfe. She met Molly Newman at the University and started a fanzine called Girl Germs. They frequented Fugazi's and Nirvana's shows to know the right people. In 1990, they were booked to performed on Valentine's Day with Some Velvet Sidewalk and Bikini Kill, which had just started. When they met the guitarist Erin Smith in 1991 they finally started playing together.
Their look is so natural and accidental that you cannot really do something to get inspiration, but if I should do a proper styling I would definitely do it like this (I found everthing on Topshop, except the sunglasses, they are vintage!):
Everithing accompanied by black fishnet tights, of course.