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On a fast wifi (or USB networking) connection, VNC is fast enough. I think the eink display is the bottleneck here. I think it takes something like 80ms to refresh the eink. VNC is faster than that.
As far as decoding HDMI, forget it. Doing it in software, in realtime, using generalized CPUs would take many many many gigahertz. You'd have to capture the stream, analyse it, decode it, etc. Even with the oldest and most primitive HDMI1.0 spec, you're looking at 165MHz of compressed datastream that has to be captured and processed.
They make specialized chips for that. FPGAs and the like that do this a thousand times more efficiently than a general-purpose CPU. You could buy one, figure out how to build a breakout board for it, try and attach it to some bus in the kindle, write drivers for it and compile a new kernel for the kindle, or you could simply take something that already has HDMI input, and run a VNC server on it.
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