Hi @abeeralam,
Unfortunately, from your conversation with GoDaddy, it appears they are not familiar with Cloudflare! If you point your nameservers where they are asking, you will no longer be using Cloudflare!
What you can do for testing is to pause Cloudflare on your site when you encounter the issue which may help you/GoDaddy to see the issue.
Also, some info on the error:
A 524 error indicates that Cloudflare made a successful TCP connection to the origin web server, but the origin did not reply with an HTTP response before the connection timed out. Review the suggestions in this Community Tip for troubleshooting ideas.