I think, it's promising generally, that you succeeded in transmitting and acquiring the image to the FPGA. This demonstrates your ability of basically facing the challenge.
The first suggestion is of course to keep the digital data cabling as short as possible (the application may require a certain length, however).Using a flat cable isn't bad, but you should have some more ground wires, up to possibly one ground wire for each high speed signal This may be already sufficient to solve the issues. It would be helpful if you can check the signal waveforms with an oscilloscope, although usual passive probes distort the signals due to capacitive load. But it's an important tool to optimize e. g. termination resistors and find the cause for transmission errors.
Understanding the said transmission problems and possible solutions, to my opinion is centered around understanding the properties of transmission lines in pulse transmission and basic effects as reflections, termination and impedance matching. There are many introductions to high speed electronics dealing with this topics, but I find it difficult to give a particular suggestion. May be other forum members can.