This sounds good. You can put 2 different floors in the Kitchen and Dining Room. Yes, it's a galley-type set-up.
Since the kitchen is small (relatively speaking), have it professionally done by a contractor that does PREDOMINATELY vinyl flooring. It's not that much to have done. If you get all the appliances out yourself, then you'll save a few $$$. I recommend that you have the baseboard trim removed too. Otherwise, the vinyl will butt up against the trim and you'll need a shoe molding installed. (This would involve, perhaps, painting or staining. And in either case, it will not exactly match ...)
I wish I could suggest hardwood or laminate or Pergo in the Kitchen. Maybe others, again, can convince you otherwise.