Here is a quick tutorial for you on how to delete stories in Snapchat.
Step 1: Start by going to your My Friends screen in the Snapchat app and tap on your name at the top of the list.
Step 3: Touch the gear of the selected Snapchat Story section you want to delete.
Step 4: When you see the list of choices, tap ‘Delete.’
That’s it, you are done. You can repeat same steps to delete all Snaps in the Story.