Earlier, the app did not allow to delete the Instagram account.
Apple has updated its App Store Review Guidelines.
Users need to sign on via web online window on desktop or mobile to delete the account.

However, the option to delete an account is only available for iOS and not for Android.
you’ve got the option to stop Instagram from removing the account.
This also comes under Apples guidelines.

If they launch the app again within 30 days, then Instagram wont delete their app.
iOS users can delete the app by following the steps.
From the app go to Profile section » Account» Delete Account.

Then you will see two options delete or deactivate your account.
opt for option you prefer.
In the screenshot, we can see, still, Instagram highlights the deactivation option as a primary choice.

It encourages users to select it.