You can. I used to be in a similar situation, and I used an ssh connection from the server to the client to set-up a SOCKS proxy. You can set it up straightforwardly with the aid of the flag -D port number (for instance 10001) when making an SSH connection from the server to the client.
(on the server, make a SSH connection to the client and leave this open:)
ssh -D 10001 client
Subsequently, you can use proxychains in another terminal to allow programs to make TCP connection to the outside world through the newly created SOCKS proxy. The configuration of proxychains is very straightforward, just add one row to your proxychains.conf file:
socks5 127.0.0.1 10001
to notify the proxychains how the proxyserver can be reached.
After that, you can use proxychains in the following way, for example to tell wget to use the proxy:
proxychains wget address
As soon as you close the first connection, the proxy ceases to exist.
You didn't mention whether you are able to connect from the server directly to the client (maybe due to firewall settings you can't?). If that is the case, you could still use this method, although you could make a reverse tunnel first:
(on the client, make an SSH connection to the server and make a reverse tunnel:)
ssh -R 9999:localhost:22 server
This makes a connection to the server, and creates a port (in this example 9999) that connects back to the client on port 22 (defaults SSH port). On the server, you can then make a connection to the client connecting through this tunnel:
ssh -p 9999 -D 10001 localhost
If you don't want to set-up a SOCKS proxy altogether, then you are probably better off making an SSH connection from the server to the client, and make a local tunnel (with -L) to the destination if you only want to reach a specific server.