Rank 6 Chocobo to Rank 7 (HELP ME)

[ChameleonMS]

You need to inbreed (parent / child or siblings) your birds to maintain its stats. You should only be breeding with stable birds if do you are missing stars.
As for MGP management, just use Tier 2 food while you for a levelling bird to Rank 40. Tier 2 food can be crafted or purchased from the MB with Gil.
Your bird stats no have bearing on breeding, only it's parentage stars.
Do not worry about MGP, you will be swimming in it once achieve your perfect P9 4* bird. You'll get 500K+ MGP from the challenges alone and the levelling to Rank 40 process at P7-9 is usually good for 50K each.

Here is a good Breeding Guide.