You get Cut from SS Anne in Vermillion City.
Flash can be gotten only after you've made it to Vermillion City. You need to go east to Diglett's cave and travel all the way through it. After you make it out you should see a big house in the south that you need cut to get in the big building I mentioned you will see two people, one who looks like a youngster, and one of Professor Oak's Aides. The Aide is the one who will give you the HM if you've caught more than 10 different species of Pokemon.