PetaPixel posted a step by step tutorial of how to save your Instagram photos without actually posting them on the app. The process is pretty simple and it all has to do with putting your phone on Airplane mode.
Once you have your phone in Airplane, open the Instagram app, take a picture, choose your filter and whatever else you want to do to the photo. Once you are done simply hit Share and it will tell you that your it failed. Just remove the photo and then check your Camera Roll.The photo should be there without having ever been in your Instagram feed.