This article explains two ways to delete your Instagram account. You can do this through Instagram's deletion page or through Meta's Accounts Center; both methods only work in a web browser.
How to Permanently Delete Your Instagram Account (Quick & Easy)
You have to delete your account through Instagram's dedicated site in a web browser. You can't do this through the mobile app.
In a web browser, navigate to the Delete Instagram Account page and log in if necessary.
Next to Why do you want to delete, click the drop-down arrow and select a reason.