If the animal is in the Shop, then it will be available for breeding. Once the animal is removed from the Shop, you will no longer be able to breed it. You can achieve this by breeding two animals that collectively contribute the Dark and Nature types. Once the Summer Equifox has been removed from the Shop, you will no longer be able to breed it, which is why it has the "not available through breeding" text because it's usually not breedable.
If you're experiencing any issues with your account, please submit a ticket to Support at Storm8. Link is in my signature