Yes, selling used brass is perfectly legal and very common. But you need to realize that not all "brass" is actually brass, there's a lot of steel and aluminum cases out there too, and those are worthless except as scrap metal. And rimfire cases can't be reloaded.
There's also "Berdan" primed brass, which is next to impossible to reload efficiently and most people don't want it. Berdan brass will have two very tiny "snakebite" looking holes in the bottom of the case, instead of one larger hole in the center. It's very hard to deprime those, and finding primers is a real challenge. Most guys won't mess with it unless it's some really obscure and hard to find caliber.
But Berdan brass, rimfire brass, and damaged brass cases do have good value as scrap metal, if you can collect enough of it.
Also be aware there's a lot of competition out there, lots of people selling brass these days, and the most common stuff like 9mm and .40 S&W sells cheap. .45 acp runs about a nickel apiece, big rifle stuff like 7mm Rem Mag or .300 Win Mag may be upwards of 15-20 cents if once-fired and in great shape.
Don't plan on retiring from it unless you can get truckloads for free! And have free labor to sort it all out. And most buyers will want pistol brass 500-1000 pieces at a time, but will buy the big rifle stuff in 100 lots too.
Lord knows I've bought several thousand cases of many different calibers over the years.