Essential scrap website provide information about power driving of theses screen, but I was more interested in the signal driving, so I choose to use the TI TPS65185 IC http://www.ti.com/product/TPS65185 which manage everything (special thanks to @Arthur Admiraal for his design https://hackaday.io/project/7153-squidpad which I partially reused).
I used ICE40 because of the open-source toolchain available http://www.clifford.at/icestorm/
The memory permit to include a framebuffer, my Verilog implement a small SPI interface to communicate with the controller.
To simplify the development, I finally created my own little tool https://hackaday.io/project/14864-ifusb
The board is specificaly made for Kindle 3 display (ED060SC7), but should works with some other display from this generation (ED060SCE found in Kobo) which are 6" 800x600 16 colors.
Hardest part was to implement "waveform" which permit to make smooth and fast transition between screen refresh.