Thanks for working on this.

I tried building with that patch, and had problems because your email 
client munged the patch. I cleaned it up by hand and arrived at the 
attached patch instead. (It needs a better commit message of course.) 
Maybe next time you could attach the output of git-format-patch.

Although the resulting system builds under Fedora 24 x86-64 with GTK, I 
can't tell any difference in flickering. I don't see much flicker 
without the patch, or with it. (I am using X, not Wayland.) Maybe my 
eyes are not good enough....

I don't see the need to expose double-buffering to Lisp via 
x-double-buffered-p or inhibit-double-buffering. Unless there's a 
demonstrated need, I'd remove these from the Lisp interface, to simplify it.

The configure.ac change should use AC_CACHE_CHECK.

set_up_x_back_buffer should be a static function, since it's not used 
outside its module.

In C code we typically use comment /* like this */, not // like this. 
Also, the spacing for pointer decls is typically 'type *id', not 'type * 
id' or 'type* id'.

You can assume C99 for loop control, e.g., 'for (int i = 0; i < n; i++) 
...'.

Thanks again.