I doubt that the code itself has a limit < 16384, just the help file.
This isn't a change I want to make in 31DEC04 with no way to test it.
Try editing
$AIPS_ROOT/31DEC04/HELP/FLATN.HLP
The line
IMSIZE 0.0 8192.0 Output image size in pixels
should be
IMSIZE 0.0 16384.0 Output image size in pixels
Let me know if that works...
Eric