Sometimes, the squadron Form 540 contains photographs of crews on arrival. It might be worth spending a day at Kew going through the Form 540.
Another approach is to get the Record of Service for Sgt Chapman and this will show all units on which he served and the dates. The same approach could then be made. As a flight engineer, it is probable that Sgt Chapman was trained at St Athan and the course photographs might have survived with the Forms 540 at Kew. Incidentally the Forms 541 will show Sgt Chapman's flying record with 12 Sqn and hence whether he was a regular crew member.
Are there any published books dealing with 12 Sqn's war service? These sort of books frequently contain crew photographs.
Sometimes, local newspapers of the time displayed photographs of local men who were killed or missing. Try the newspaper archives in Sgt Chapman's home town.
I guess from the initial post that this is probably a busted flush but are there any siblings of Sgt Chapman or other family who might have photographs? Does the secondary school at which Sgt Chapman attended still exist and do they have any photographs of pupils, perhaps in the final year?
Old Duffer