Take the picture, apply your filters and share the photo to Instagram. When you do that, the edited photo is saved to your camera roll as well. Once done, simply delete the photo from Instagram.

You could also keep your profile private so no one would ever have a chance of seeing the photo while it was briefly posted.

I checked both the Android and iOS version of Instagram but found no option not to upload photos to Instagram once taken with the app. If you do not like to upload to Instagram but would like to use filters for your photos, just use other photo apps such as EyeEm or Camera+.