Circuit requirement for Arduino Due custom circuit without the ATMEGA16U2
Since you have USB you just connect it to your computer. As long as the flash is blank (use the erase button) it will enter the BOSSA bootloader at powerup and you can use the Arduino IDE to upload the code as normal (or the bossac command line tool).

There are two ways of entering the bootloader: 


Wipe the flash with the ERASE button (or trigger from 16U2). 
Open the native port at 1200 baud. 


The latter is only possible if you have first programmed the board with a sketch with that ability in it. The most sure-fire way is to include the erase button.

You can either provide a physical button (as shown in the existing schematics) or a simple jumper that can be shorted when erasing is needed.