Why should I cook the flour first when making bechamel sauce?
This link explains the science behind what is known as "the mother sauce", béchamel.  Essentially, the steps of first creating a roux, then adding cold milk, are about manipulating the glucose chains in the flour.  Done correctly, the sauce is smooth and flavorful.  Done incorrectly and you have a grainy mixture that tastes of raw flour.

@David Richerby's comment below prompted me to investigate further.  So, I turned to Harold McGee's classic, On Food and Cooking.  He writes, on page 617, that:


  in addition to coating flour particles with fat, making them easier to disperse in a hot liquid, roux making has three other useful effects on flour....it cooks out the raw cereal flavor, and develops a round, toasty flavor...second, the color itself...and third, heat causes some of the starch chains to split, and then to form new bonds with each other.


He goes on to explain the importance of this step, but it generally achieves the desired texture and means the sauce is less likely to congeal on the plate. 

From Wikipedia's page on starch:


  Starch or amylum is a polymeric carbohydrate consisting of a large number of glucose units joined by glycosidic bonds.


...and, yes, this correlates with gelatinization.