There are three basic methods of thickening with flour: A roux, a slurry, and beurre manié. Slurries have, as far as I can tell, gotten a bad rap, and are no more prone to making a dish taste "floury" than any of the other two methods. The key to removing the starchy taste is to cook it a couple of minutes. The way the flour is introduced is irrelevant. One tablespoon of flour thickens one cup of liquid.
A roux is a 1:1 combination of melted fat and flour (when you make gravy, you make a roux), into which liquid is added. Cook it over medium to high heat, stirring constantly, until it thickens.
A slurry is a combination of flour and liquid, stirred into hot liquid. Stir constantly and cook it until it thickens.
Beurre manié is a combination of soft butter and flour, kneaded together (hence the name, which translates from French as kneaded, or handled, butter). Directions for making a beurre manié always specify that you roll it into little balls. This is silly and unnecessary. In fact, I use a flat whisk to blend the butter and flour, and since the mixture globs onto the whisk, I just use the whisk to stir the sauce. It works perfectly well. Forget the little balls. Mix it, then whisk it into the sauce. Again, you have to stir constantly until it thickens.