You cannot delete your Gaia account. From their FAQ:
“We do not completely delete accounts on Gaia, as we need to keep a minimum of information on file for record-keeping and dispute-resolution purposes. If you would like to remove information from the account, you can log in and do so at any point by going to My Gaia, then to Account Settings. There you can change the email address on the account and update the password. You can even change the username on the account, if you want.”
You can, however, use this form to partially delete your account:
STEP1. log in to your account.
STEP2. Now visit https://www.gaiaonlinehelp.com – you need to do this first because Gaia online sets some weird cookie that possibly blocks access to the link below.
STEP4. Choose “General Account Inquiry” from the first select box.
STEP5. Then “Account Status” from the second.
STEP6. And then “Delete My Account” from the third. Politely tell them to remove your account.
STEP7. Finally, click “Finish” to submit your ticket.