Unable to access one server on network, while able to access others

I am not certain about the terminology; I will try to be as clear as possible but note I might use a word wrong.

I have a number of Ubuntu servers, all connected to the same network. I can access each of these servers over SSH, but only if I am connected to that same network via VPN.

Background:

I am trying to run licensing software which is supposed to serve the license to the other servers on the network. The license software appears to run correctly on the designated server and that server is also able to access the licensing software. Any other server on the network is unable to connect to this server running the licensing software.

To troubleshoot this network problem, instead of troubleshooting the proprietary software I tried to run simple Python Flask servers on each of the servers. Similar to the proprietary software, Flask appears to run properly but I am not able to connect to it from another server on the same network, but I am able to connect to it from the same server.

The problem:

When I run a simple "hello world!" Flask server on Server_1 or Server_2 with host=0.0.0.0 and port=5000 I am able to connect to Server_1 and Server_2 from every other server using ip_of_Server:5000.

However, if I run the same Flask server on Server_3 with the same parameters I am not able to connect to it from Server_1 or Server_2. The error I get from trying to connect via wget is failed: No route to host.. When I try to connect via Chrome I get ERR_CONNECTION_TIMED_OUT instead.

I am also always able to connect to localhost:5000 from each of the servers. I.e., I'm able to connect to the flask server running on Server_1 from Server_1 via localhost:5000, but I am unable to connect to the flask server running on Server_1 from Server_2 via localhost:5000.

What I tried:

I initially though this might be a firewall issue.

I tried to 'disable' iptables using the following:

sudo iptables-save > /root/firewall.rules
iptables -X
iptables -t nat -F
iptables -t nat -X
iptables -t mangle -F
iptables -t mangle -X
iptables -P INPUT ACCEPT
iptables -P FORWARD ACCEPT
iptables -P OUTPUT ACCEPT

This did not seem to affect the issue. I also tried sudo ufw disable, but equally, this did not affect the issue.

This leads me to believe it is not the firewall, but I am not sure if this is true. I also so do not know how to continue debugging this issue.

The output from wget, 'No route to host', means that neither Server_1 nor Server_2 have a 'path' to Server_3, this isn't a firewall issue or a flask issue but more an IP (Internet Protocol) issue.

To fix this I suggest making sure that you can 'ping' Server_3, ensuring that it is connecting to the internet and that when using wget you are using the correct IP address, further detail would be needed to properly point to the error, like running a traceroute.