I had the same problem with my SONY KP51HW40. The problem started about a year and a half ago, image turning greenish, then back to normal. Then started getting worse, with the image turning greenish or reddish, and then flashing green once and continue operating normal. And finally, it got really bad with the set shutting off after flashing green several times. It would not operate for more than five minutes at a time, before shutting itself off. So my problem got to the point of needed attention and here's how my TV got fixed.
I downloaded the service manual. After the TV was shutting itself off, it displayed an error code using the POWER/STANDBY LED. My TV set STANDBY LED was flasing 8 times, and according to the service manual, this means that the T8005 transformer was bad. This is the high voltage transformer that feeds all three CRTs. The solution was to replace the transformer, but I am not really good at soldering so I decided to replace the entire D-Board, which is where the T8005 transformer resides. This transformer is also called the flyback transformer. So I ordered the new board and replaced it myself. This is the high voltage (30,000 Volts) transformer, the CRTs can hold electrical voltage for a long time. If you are not familiar with TV repairing, you can be seriously or fataly injured. That is my disclaimer.
After replacing the D-Board, the problem was not solved. Obviously, the SONY diagnostics circuitry read low voltage out of the transformer and assumes the transformer went bad, but they don't tell you what else could be the problem. If the transformer voltage drops, it could be because of not enough current coming into the transformer or a short in a circuit at the output of the transformer. Then thinking, if I had green flashes (not red or blue flashes), it was clear the green CRT was the culprit. I unplugged the TV set, a couple of days later I started checking connectors and noticed the CG board (the board at the end of the Green CRT; the Green CRT is the middle CRT) was a bit loose compared to the Red or Blue CRT boards. So I pulled the board out (pull down while jiggling, no latches). Clean it well. Then I slightly bent the CRT pins, very carefully, very slightly, outwards (away from the center core). I re-inserted the board and this time, it was much tighter, and the pins were making better contact with the CG-board socket.
Turn the TV on, and problem solved. No more green flashes, no more TV shutoffs.
The SONY service manual did not do me any favors with the diagnostics. It should've listed all possible problems, including faulty transformer, short on CRT, bad connections, cracked cold soldering, etc. Lesson learned, and now I ended up with a spare D-board because SONY parts sales are always final. No refunds.