Tap Accounts Center, then tap Personal details. Tap Account ownership and control, then tap Deactivation or deletion. Tap the account you’d like to permanently delete. Tap Delete account, then tap Continue.

Here’s how to permanently delete your Instagram account from the phone app:

Tap your Profile > Menu > Settings and privacy > Accounts Center.
Tap Personal details > Account ownership and control > Deactivation or deletion.
Choose the account you want to delete and select Delete account > Continue.