First, everyone has slightly flappy upper arms, even athletes and models so don't be too hard on yourself.
It is impossible to spot target fat areas, your body will naturally lose weight and size in the opposite order it was put on. If you are fit everywhere else then you should focus on muscle toning. Focus on your entire arm and shoulder area, but especially the triceps, deltoids, and biceps. You don't say where you workout, if you go to a gym ask for help finding machines and weights that focus on those areas (most machine are labelled with what muscles they work), if you workout at home search the internet for at home exercises that target those muscles.
Short of plastic surgery that is your best bet to firm up your upper arms.