Pop to the profile section in the app, click on More and follow the close account instructions from there. Alternatively, 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.
Your feedback is important to us, so we may ask you for the reason you wish to change your preferences or close your account, this feedback could help us improve our product.