So I want to modify this board in order to add a 40 pins tft connector to drive a 5" LCD 800x480 display so the user can "flip" between HDMI and TFT. I have no idea where to start, could you give me a clue?
You can't. (At least, not without ugly workarounds like adding an HDMI switch and a HDMI to TFT decoder.) The Allwinner H3 is designed as a TV set-top box controller; it only supports HDMI and CVBS (composite video) output, so it cannot drive an LCD directly.
Some of the other parts in the Allwinner SoC family, especially in the "A" series, do support LCD output. Whether they will be appropriate for your needs is for you to determine.