Flonase isn't a generally accepted medicine for treating sinus infections but Flonase can still be used to treat a sinus infection if you want too since it will work to clear up a sinus infection.
Nasonex and Rhinocort will also work to clear up a sinus infection by promoting drainage and reducing inflammation.
If you have a sinus infection you should also use a humidifier or vaporizer to add moisture to the air or even take a steamy shower or just sit in the bathroom with the shower steaming up which can help your sinuses and sinus infection.