Isn't there a door you can put it in? We had a similar problem with a cat flap and ended putting it in the double glazed doors. Expensive, but worth it as it stopped all the arguments we were having about letting the cats in.
We viewed a house a while back where they had a dog flap in the external wall. It was big - maybe a foot in height? And a little tunnel like. The flap had fallen off so it was literally a hole in the wall. The estate agent called it one of the house's 'unique' features! It didn't put us off on its own but there were quite a few 'unique' features that certainly didn't help!
I had a cat flap put through an external wall in my old house (Victorian terrace so walls were not thin!) A handyman did it. We got a standard cat flap but with lots of extension pieces to make it into a tunnel. In retrospect, it perhaps was not the best idea as it might have put people off when buying the house as it would have been a pain to block up again.
We are in the process of moving house and our next property has no obvious door for a dog flap. Having had the convenience of one for the last 20 years, we (let alone our dogs!) couldn't contemplate NOT having one. The kitchen has plenty of outside walls which could have a dog flap put in to access the back garden but I'm not even sure if this can be done?! I assume it would be like a little tunnel? Would this be something that a builder would need to do? TIA