I recently received a Due, a 2.4" TFT and a CTE TFT controller with on board SD.
I was able to use the UTF libraries to display things but I had trouble getting the SD to read using the SD libraries. After a bit of research on the shield I determined that jumper 8 needed to soldered closed allowing pin 53 to become the CS pin.
I failed using the ITDB02_tinyFAT16 and the demo example to display raw files because the library, as of this date, does not support the DUE. Having a bit of experience with Adafruit libraries and the SD library I opted to modify the bmpDraw routine from the Adafruit TFTLCD library example TFTBMP.
I can now display bmp files. I have placed the code on GITHUB at https://github.com/mboroff/UTF_Display_BMP_Files.git. Feel free to take a look.