Ah yes, the dreaded arm flab. This is a problem for quite a few people, but not one that can't be fixed. Getting rid of body fat under your arms is no different then reducing body fat from anywhere else. First and foremost, to reduce body fat you must consume fewer calories than you burn on a regular basis. A sensible, lower calorie diet combined with regular exercise will do the trick.
Cardiovascular exercise is a great way to burn off some of those excess calories. Swimming, riding a bike, running, jumping rope, and even walking are good examples of cardio exercise. As far as your resistance training is concerned, it would be misleading to say that performing arm specific exercises will get rid of arm flab. There is no non-surgical way to spot reduce body fat from a specific area by targeting that area with exercise (arms included). A better strategy would be to work your entire body with resistance training, since having new lean muscle throughout your body will help speed your metabolism. Resistance training burns calories during the workout itself, and more importantly sets you up to burn more calories all day, everyday. Reducing arm flab = Burning calories!