Any success stories with flabby arms?

Do you still have weight to lose? If so, that will make a signficant difference.

Beyond that, I find that most women (every single one I've discussed this with in real life, in fact) are misidentifying relaxed triceps muscles as part of their loose skin or fat. I ask them to stretch one arm out straight, then take the opposite hand, and grab the "loose skin" "chicken wing" "bingo wing" "flap" on the extended upper arm, putting their finger tips close to the upper arm bones, and hold on.

Next, I've had them flex that extended arm in as "bodybuilder-like" a pose as they can accomplish: Upper arm above shoulder level, elbow bent, hand curled down/in toward the inside of the arm, consciously/conscientiously tightening every single muscle they can feel, especially those underneath the upper arm. Anything that firms or tightens up when we do that is muscle, not fat or loose skin.

I'm not saying there's no fat or loose skin. I'm saying that in many cases, a big chunk of what women identify as fat/loose skin is actually relaxed muscle. It's 100% normal among even quite fit women (and men) to be able to extend an arm horizontally but otherwise relaxed, shake it hard, and get some floppy mobility in the upper arm. If relaxed muscles were tightTight, how would we move our skeleton around? Relaxed is relaxed, so somewhat slack. The long muscles, in a horizontal position, relax and hang a bit, under the influence of gravity. (Thighs will do the same thing, but we don't usually see them in the same way.)

(That women often misidentify their triceps and hate them as part of their "arm flaps" is one of my pet peeves. )

So, figure out what part of your upper arm is actually fat, as above. It's probably less than you'd think. Losing weight overall will help reduce the fat part of it. After the fat is lost, the loose skin part of it will start to shrink, and that will take some time to happen (maybe slower than fat loss, but you appear to be young, so your odds are pretty good that it will happen in the first year or so after you hit goal weight. You can firm up the muscles in that area for some other moderate benefits.

A compound exercise that works multiple muscle groups would be best (overhead press/shoulder press, bench press, push-ups and variations; and there are others). It's also possible to do accessories like tricep extensions or tricep dips, and others. (You can look those up).

Don't expect that relaxed triceps will be firm under all conditions, even once very trim and strong, though. You need some slack in there to be able to move your arm. (Our thighs are kind of the same; but they're mostly vertical, and the slack is at the back, so we don't so much notice.)

Best wishes!