If you ever want to delete your Snapchat account vs. deleting any pictures or videos that you posted that automatically disappear you have to actually go to Snapchat’s website in a browser to delete your account.
First go to .. https://www.snapchat.com/ and in the footer click “Support” which will take you to this page..
FYI (you can scroll down to the bottom of this post click “login” link and it will take you directly to the login page to delete your snapchat account)
Then in the left side bar click on “My Account & Settings” which will take you to this page where you will want to click “Account Information”
Then after clicking on “account information” you need to click on “Delete my Account” which will then ask you to login with your user name and password and bam “delete your snapchat” account completely.