We just changed our nameservers from GoDaddy to Cloudflare. Is it ok and safe for us to delete our sites from GoDaddy and close our accounts there now?
Welcome to the Cloudflare Community. 
Your post lacks sufficient information for anyone to be able to objectively answer your question. If you purchased your domain name registration, your webhosting, or your email through GoDaddy, it would be very unwise to close your GoDaddy account, as it would prevent all of those things from working.
If you care to provide more detail, such as your domain name and what services you use at GoDaddy, you may be able to get a more detailed answer. Until such time as you know exactly what will be impacted by that move, I would encourage you to curb your enthusiasm toward cancelling your GoDaddy account, no matter how thrilling the prospect may seem. 
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