For the GUI to work on the kindle, it needs eink support. Even if it has framebuffer support, you need to trigger eink updates. That can be added to the code, or it can run as a background script the way Jesse Vincent did it for Savory (Qt/Calibre ported to run on the kindle).
Depending on WHICH kindle, it needs some input handling too (DX and K3 use different keycodes for their keyboards, K4 needs a 5-way joypad controlled onscreen keyboard, K5 needs a touchscreen onscreen keyboard and touchscreen mouse emulation). None of these are trivial.