Okay, the flabbiness is a function of genetics. If your mother and grandmother have it, you'll probably have it. You probably have some degree of it now. Why? Because women typically don't pay attention to muscle building. All you are seeing on the underside of your arm (triceps) is small muscle tissue wrapped in subcutaneous fat that is subject to gravity. Almost all women have it. Now, there's only two ways to get definition: either lose subcutaneous fat or bulk up. The term bulking up scares women. But to get definition you have to build muscle tissue which is the same as bulking up. You combine bulking up with a reduction in subcutaneous fat. For your triceps, do tricep pressdowns. They're convenient because you can control the weight, both poundage and motion. A trainer at the gym can show you how to do them and recommend sets and reps. The foregoing is true for any body part. Give it a shot.