Its the one thing that doesn't seem to have been transfered now. I have found that if you want to use it, set it up on PS3 and it will appear on your soldier on PS4 even though it doesn't show as an option. Less than ideal, but you can still equip patch and background while you wait for a fix.
We are aware that players are not receiving certain DLC when digitally upgrading. We are currently looking into this and we will update the community once we get more information. We appreciate your patience through this time.
Also, thank you for the feedback! We are always looking for ways to improve player experiences with Ghosts. I will continue to monitor suggestions to have the Call of Duty app implemented for PS Vita use and will forward accordingly.