That’s odd, I don’t think you’re missing anything.
Some users who have had iPhone connection woes report that they had to reboot their phones after downloading the app to get it to work right. Have you tried this? Also, the Mooshimeter can only pair with one device at a time, so make sure it’s not connected to the iPhone 5 when you try to connect it to the iPhone 6.
Hope this is helpful, please let me know how it goes.