If your web solution uses Cloudflare as CDN in front of Azure App Service, then all web browsers connect to Cloudflare content servers first, and then the actual web pages are pulled from Azure App Service by Cloudflare.
In this manner, the Cloudflare header is in fact generated by Cloudflare servers, and it is impossible to disable them on Azure App Service side.
Please contact Cloudflare and ask them for assistance.