Pop to the profile section in the app, click on "More" and follow the close account instructions from there.
Have you considered that instead of closing the account, you could:
Change your preferences on how you use the app and Sling communicates with you, for example; you can toggle on and off your preference to be located in the Sling Directory -check it out in the profile section of the app,
Unsubscribe to e-mails sent by Sling - just click that option in the email,
Uninstall the app from your device and re-install & sign back into the account at a later stage.
We value your feedback, so we may ask you for the reason you wish to change your preferences or close your account.
If you would also like to have all your data deleted, please contact us via in-app chat.