First of all it an interesting setup. Out of personal interest: Whats your motivation to build something like this?
As far as i can see this is not possible:
When connecting to server 1 you could use "redirect gateway" and therefore use the external ip from server 1.
Having this connection you could start a vpn-connection to server 2, alltough, :
- if you do not redirect gateway, your external ip will still be the one of server 1
- if you redirect gateway in the second connection, you will lose your connection to server 1 as you cannot have 2 redirected gateways. And therefore loose connection to server 2 as is went through the tunnel of server 1
This still holds 2 vpn-servers and not 3
If, on the other hand, you first connect the 3 servers into a chain together and connect to the first one, you cannot use a redirect gateway as is will point to the first server, unless you do a ip-forward from the tunnel-traffic to server 2, through the vpn between server 1 and 2. And on server 3 the same again and an outbound NAT to use the external IP from server 3.
In the second setup it might me possible to chain them together, the question is if this is what you want to achieve. server 1, 2 and 3 can all see the plaintext traffic. If that's not an issue, you might want to go down this path.