No exercise for any muscle group is going to burn the fat in the area. Lifting weights is going to build muscle in whatever area you train. Fat loss comes from eating in a calorie deficit. You also cannot spot reduce fat, so if you are eating in a calorie deficit and losing body fat, you are going to lose it throughout your entire body. If any video online is telling you that an arm workout is going to get rid of fat in a certain area, they are absolutely lying!
Instead of doing a calorie deficit i’d encourage you to simply eat better with more protein and such while also boosting your cardio. this is what i’ve done (no calorie deficit, if anything I eat more than I used to) and i’ve lost a noticeable amount everywhere, including my arms which used to be quite big.