Ok I think I worked out a part of it. I need to use the OUTPUT channel in the "nat" table, from my client machine.
The server uses a squid proxy.
iptables -t nat -A OUTPUT -p tcp --dport 80 -j DNAT --to-destination 22.214.171.124:8080
The only problem now is that it is a Authenticated proxy. I need to supply a username and password somehow.