Linux – iptables FORWARD packets from one chain to another

You're sending the traffic to 10.52.208.221. Given the config you posted, your problem is the webserver, not the firewall. Your rules look to be correct. FORWARD and INPUT are redirected to RH-Firewall-1-INPUT where your first rule is to allow all traffic. As somebody else pointed out, you could be allowing all traffic on eth1, while the world is actually coming in eth0. Secondary, you have to NAT the traffic as it goes back out to the world

iptables --table nat --append POSTROUTING --proto tcp --dport 80 --jump MASQUERADE -o OUT_INTERFACE

Your traffic originating from the router will never hit the input or forward chains, but instead traverse the output chain on to the webserver. Other systems in that subnet will similarly go directly to the webserver. Systems out on the world at large however will traverse the INPUT / FORWARD chains and need SNAT as well as DNAT so that it appears to the world to be one machine. You still cannot test from within your network. you must test from the opposite interface from the webserver. Get me your IP addresses and I'll point you to the proper configs.

Looks like I was using the wrong IP address. My hosting provider identified the true IP of the server upon which my VPS was residing. I entered that, and everything worked like magic!