I've always owned Hale pet doors and have had both the single and double flaps. We currently have a single flap for a cat on a door facing southwest (our worst weather/winds) and it has yet to blow open in a wind and keeps all rain out. For a larger opening I would have used a double flap.

Hale is expensive but they're built to last. All metal frame plus the flaps are so quiet with no clanging of magnets as they open and close because Hale doors are lined with nylon 'brush' weatherstripping. The frames are not bulky, unlike a lot of the plastic frame doors...and you can buy replacement parts.

Here's another brand comparable to Hale, but the flaps don't appear to be as weatherproof. Not sure since I've never owned the brand.

Definitely stick with a brand that has vinyl flaps vs a solid swinging door. I once had a dog change her mind after getting half-way thru a solid flap door. She nearly ripped the frame off the door!

Also, price check the web. I found a company that was much less than any of the major pet suppliers.