I had been using an iphone, and had lots of important waypoint routs set.
I just got a new monitor, the Nvidia Shield K1, and when I tried to fly the same routs that I bad been before, apparently they are saved to the iphone and not the intelligent flight batteries?...

Is there a way to transfer these saved flight paths to the new monitor?

Not possible.  May have had a chance had you replaced your iPhone with an iPad and not an Android device.  Could have backed the Go app to iCloud and that downloaded it to the new iPad.