I've had the same problem and think I found a solution - hope it helps. When I "import" the AirBnB Calendar Link to Booking.com, I get the following error:
"This isn't a valid iCal URL – please try again."
For some reason Booking.com does not recognise it. Strangely enough (and I don't know why this is), if I go to Home Away (copy the AirBnB link I added there, which works) and then go back to booking.com pasting that, it seems to sync.
So go to any other platform (and copy the imported AirBnB link from there, instead of exporting it from AirBnB) and past into Booking.com.
This at least worked for me...