After installing node red on the new system and running it for the first time, copy the whole of the .node-red folder except the node_modules folder from the original system to the .node-red folder on the new system. Then in a command window go into the .node-red folder and run npm install
which will install any extra nodes you need.
Then restart node-red and refresh the browser window if you have one open.
The default flows file name changed some time ago. Are you sure the new one is not called flows.json (you posted flow.json)
Delete the new flows and cred files and rename the old files to match the new format.