Help Me Rid My Gas Tank Of "Rust-Flakes"

[Cor66Vette]

So I'm cruising down the road after not having driven the car in many (many) months and all of a sudden...dead in the water. I pull over and after about 1 minute or two, I am able to start the car. I get it home- only about a mile- and the car stalls in the driveway. After a few minutes, I can start it and I get it into the garage. I open the gas cap and notice a whitish buildup on the inside of the gas cap. I clean it off and before I screw it back on I look inside the tank and find clean-looking gas but the bottom of the tank is laden with what appears to be rust flakes. What's the correct way to get the tank clean and I hope the answer isn't to drop the tank. Your advice is needed and most appreciated. Thanks in advance.