Sadly, you can't disable Cloudflare on a per-directory basis with a page rule: By the time a request is matched to your page rules, it has already reached Cloudflare, and will keep causing an error 520 even if you disable Cloudflare cache on the directory.
Yet, you can disable Cloudflare for a specific subdomain, so you may want to create that page rule to forward the requests to another URL, that one being behind a subdomain not on Cloudflare?
Still, errors 520 can be fixed. Their detailed explanation is here, but the short version is that your webserver is either:
- returning headers bigger than 8KB (typically the case when there's a lot of cookies)
- prematurely closing the TCP connection coming from Cloudflare