This is my approach to fixing peeling shoe sole layers. I cleaned and even Dremeled the inside layers of rubber to help glue adhere, but I was like "How the hell should I apply pressure while glue dries?"...
So I figured I should easily be able to do that with some thumb tacks in the sides of the sole, and temporarily stitch it down with dental floss for a day or two while the glue dries.
Wish me luck, I used silicone glue. Not sure if that's the best glue or not for the purpose, but it's tough and flexible. Of course I did both shoes, just figured it would be more obvious what I did with one shoe showing the initial damage.
Anyways, thumb tacks and dental floss for the win to hold it together while it dries!
Edit: Confirmed, my fix is solid, even holding better than the original factory glue! Haters gonna be haters though, carry on with your downvotes if you want. Just sharing my technique of salvaging shoes for less than $5 of glue and stuff around the house.
I use that same silicone stuff all the time to make repairs and non-permanent attachments of things to other things. I'm guessing it will work OK for this, but over time it might peel apart as shoes flex and move a lot. The silicone is flexible, as you said, but the adhesion may weaken with constant movement.
They make some stuff for this exact purpose called Shoe Goo... that may or may not work better. I've used it for off-label purposes like reinforcing the thin plastic shells of RC cars. It dries much harder but is still semi-flexible. It adheres strongly and won't peel off without a lot of force and a scraper tool. (Silicone can peel off using just your fingers).
Good luck, it might work out.
I've actually tried Shoe Goo before years ago, but it didn't last very long for me. So this time I'm trying a different glue and different process..