If you want to delete your Instagram account, follow the following steps to achieve this:
Sign in to your Instagram account by entering your username and password and click Log in button.
Locate your username on the top right-hand corner of your browser, and click.
From the drop down links, click “Edit Profile”
Locate the link on the page towards the bottom right edge of the settings area, that states “I’d like to delete my account“. Click the link.
Locate and click the drop-down box for the reason why you’d like to delete the account.
Click the reason you want, to select your reason. Most people select “Other“, but if a better reason is already listed, click that link instead.
Click into the “To continue, please re-enter your password” box then enter your account password.
Click the box stating “Permanently delete my account“.
The direct Link to delete Instagram Account is: https://instagram.com/accounts/remove/request/