We don’t have any restrictions on favicon.ico rewrites, however if it is hosted on a different server, you might need to update both the URL path and destination of the request for the image to be fetched correctly: Change URI path and Host header · Cloudflare Rules docs.
Keep in mind that DNS record override is only available for Enterprise zones, however you can either host your favicon at the supported public cloud storage provider and route requests to it via Cloud Connector, or you can achieve a similar result using Snippets: Change origin and modify paths · Cloudflare Rules docs.