The method to close your Instagram account from another device, will depend on whether you still have access to it or not.

I leave you a manual where they explain step by step what to do in each situation:

Log in from the device you have and change the password. After successfully changing it, you will be asked if you want to log out from the rest of your devices where you are logged in, that's where you have to say YES. That way, you will be logged out of any devices that are currently using your account, and they will need the new password to log in again.