I've sent the following to my TI contact:

Thanks for offering this.

What we need is:

After every call to the function static void Flip(OMAPLCD_DEVINFO *,
long unsigned int), there should be a ioctl made into kernel, using
OMAPLCDBridge, to the following ioctl:

#define OMAPLCDIO_PERFORMED_FLIP _IOWR('F', 0x41, struct
OMAPLCD_INIT_MAIN_IN_DATA_TAG)

A similar call can probably be seen if you look for
OMAPLCDIO_DEINIT_MAIN in your current code.

We can implement the kernel side ourselves, we just need the user code
to call this each time it has run Flip()

The reason for this to be done after each Flip() call, is so we can
start a data transfer of the framebuffer to the external LCD
controller in kernel, of the framebuffer it just flipped to.

Thank you!