Sorry Frankie's feeling unwell.
A few questions here, so apologies for all the question marks, but it may help clarify a few things. Am I right in thinking that you switched one of your other dogs to raw at the same time? If so, is he OK? If he is I don't think there will be anything wrong with the food.
Has Frankie been pooing OK? Natural Instinct has quite a lot of ground bone in it, which can cause constipation. Out of my two, Louis is fine on it but William sometimes becomes constipated and uncomfortable, which is one of the reasons I vary their raw diet. As you get more familiar with raw and as Frankie becomes fully used to it you'll probably find yourself tweaking it to suit his needs.
In the meantime, if Frankie was mine I'd encourage him to drink a little water, or carefully syringe a little bit into his mouth every so often to make sure he doesn't get dehydrated if he's still not drinking, and see how he is in the morning.
Has he ever had anal gland problems? That could be a reason for Louis trying to smell him, and anal glands can be very uncomfortable if blocked or infected.
I hope he's feeling a lot better in the morning