We have noticed this too and are looking into it. The app is the same as the iPad app and has the same app bundle identifier, so you should not be allowed to be charged for it twice, but to be extra cautious you should try these steps first.
iTunes and see if there is an 'Update' button next to Morning in the App Store. Then you should be able to update it and sync it with your phone.
You can do this by going to the App Store > Updates > Purchases > Not on this iPhone. Check to see if Morning is in this list.
Free Upgrade Message
We think the price showing up is a problem with the App Store. We also saw a price, but when we bought it got a message saying it was a free upgrade since we had already purchased it. We're pretty sure this should work if you are logged in with the same Apple ID you purchased Morning with on your iPad. If you are charged for Morning twice, let us know right away by contacting us at firstname.lastname@example.org.