Newyorker, we have two cat flaps. I love the term "Airlocks" - like yuo, we have an inner door, and an external door which form the access to the house. We have a microchip scanning flap on the front door and until recently, had an ordinary staywell flap on the inner door. We just replaced the inner flap with another scanner flap, but one that permits us to restrict Moray's access to the outside until he's much older, whilst Tinks can come and go freely.
The problem we had, was when we replaced our front door. We replaced it from an old wooden door (which we were able to fit the flap ourselves) to a UPVC door. Lucj=kily, the door company we got were extremely helpful, and even though they'd never done it previously, they agreed to manufacture the door with the flap aperture cut out for us, then when the door was fitted, their fitters also put in the flap for us.
I will also admit we have another cat flap in the door leading from the living room to the kitchen
If we ever move, I'm going to have to get a cat loving purchaser, or otherwise change the doors!