The iPhone automatically stores the photos in its storage. There's nothing you need to do.
If using iCloud Photos, it would then sync them to iCloud and they may get deleted from the iPhone if they are deleted from iCloud or another device that is logged in to your Apple ID and using iCloud Photos.
Make sure, that iCloud Photos is not turned on in Settings->Account(top of Settings)->iCloud->Photos->iCloud Photos.
Outside of that, unless you manually delete them, there is no way for them to get deleted automatically on the iPhone.