I think the way to tone up the flabby upper arm is to use a small weight behind your back (if you don't have proper weights, use something else e.g. a tin of beans to start with). Put your hands behind your head, point your elbows upwards and drop your hands (holding a weight each) down behind your back as far as you can. Then raise each weight alternately out behind you so that your elbow makes a right angle. You'll feel the under arm muscle working. Repeat about 15 times for each arm (or until it gets too uncomfortable).
It's notoriously hard to shift flab in this area but persistence will give good results in the end.
Good Luck!
Unfortuately exercising a part of the body will not cause fat loss in that area.Contary to popular belief muscle doesn't turn to fat due to lack of use it just lose's it's tone.So it's diet or surgery!
Just to add to Elfin's answer - it's really important not to arch your back, stick out your chin or snap your knees back while doing that exercise. You don't want to have toned up muscle but painful back, neck or knees as a result. Also as norfolk boy says, toning up doesn't get rid of flab - but it may not actually be fat that's the problem but just flabby muscles.