Looking at:
[31mMessage: [0m[31morg.openqa.selenium.remote.UnreachableBrowserException: Could not start a new session. Possible causes are invalid address of the remote server or browser start-up failure.
I think I have seen that when the connection to Appium is failing. Try to just leave appium running without jenkins kicking it off to see if that solves the problem. With so many working parts try to isolate which is giving the issue. Please comment on the next issue if you have one.
If you want appium to run when a test is triggered try to run it within the test itself. Then have it close the connection when the test finishes. Just make sure your tests waits a couple seconds before trying to connect since appium has a slight boot time