How noticeable is reconstructive surgery after a double mastectomy?

Variable. There are a lot of variables involved but in general a double mastectomy is a good situation for reconstruction. That is because it is easier to create two similar breasts than to have to match an existing breast. If possible learn about your reconstruction options before the mastectomy.
It depends. This answer depends on the method of mastectomy (modified-radical, skin-sparing, nipple areolar-sparing) and the type of reconstruction. The goal of reconstruction is to look "normal" when dressed in underclothing or a bathing suit. While it will look much less disfiguring than a woman who has had a mastectomy without reconstruction, it is usually obviously different than the presurgical state.