Duolingo is one of the best apps on the planet and helps you to learn any language through games. But if you want to close your account, you can do that in the Settings page of your online profile.
I’ll show you below with pictures how I managed to remove my profile on a desktop computer:
1 Go to duolingo.com and sign in
2 Click on your name and choose ‘Settings’
3 Scroll down till you see the deactivate my account link
4 Confirm that you’re sure that you want to close the account
Your account has now been deactivated and you’re free to remove the app itself from your iOs or Android device (or whatever device you installed the app on)
Source screenshots (and thanks to): duolingo.com