Yes, you can take screenshots of Snapchat on your iPhone without them knowing, by following the given steps -
1. Open Snapchat on your iPhone and load the Snap.
2. Turn on airplane mode.
3. Watch the Snap and take a screenshot of Snap.
4. To enable force stop - Swipe up from the bottom of the screen and swipe up on Snapchat.
5. Now, go to the app settings-->Snapchat-->Clear cache.