I wouldn't use the tooth brush, depending on the quality of the board, you might either break something off, or lift a pad, or dig under the lacquer causing rust.
The alcohol is fine, but in this case it's Flux that you're cleaning, flux is only somewhat soluable in alcohol.
they make special flux cleaner that you can buy.
I would stick to paper towels
Flux cleaner is expensive and difficult to use though , but it's 100% safe on the board, that's why they sell the stuff.
Alcohol may work faster, and is more practical, but it's aggressive on the lacquer and can sometimes cause rust.