The Settings page on the Instagram iOS and Android apps is where you can delete your account. Go to your account page and

tap the three horizontal line icons located in the upper right corner of the screen to get started. In the dropdown menu

located at the top of the list, tap the Settings & Privacy icon. When you click on that icon, a new page with

  an extensive tool list will open. Select Personal details under Account Settings after tapping Account Center

at the top of the newly displayed Settings page. You'll see a new page with your birthday and contact details. 

After you tap "Account Ownership and Control," the "Deactivate or delete" tab will pop up on a new tab.