Alice, it depends on what you mean when you say flabby arms.
If you're talking about excess
fat on your arms, then yes, that will go away with weight loss. When you lose fat, it will come off from all over your body, including your arms. Unfortunately, we can't spot reduce by targeting one body part with exercise -- fat comes off in whatever order it wants to.
If you mean excess
skin when you talk about flabby arms, that's a different story. If your arms were a lot bigger and now have empty skin where there used to be fat, losing more fat isn't going to make the skin go away. Sometimes time helps with skin tightening, but exercise won't make skin shrink either.
But regardless of whether it's skin or fat, lifting weights can be very helpful (and I'm talking full body workouts, not just for your arm muscles!) Weightlifting will speed up your metabolism and allow you to burn more fat. And building up your arm muscles can help to fill in skin that's loose from weight loss.
My suggestions are to add weights to your exercise routine, if you haven't already, and be patient. You may find that you don't have a problem once you reach your goal or if you wait for six months. If you still do, then you can consider other options.
Best of luck to you!