I agree with you, BOAC, regarding some of the answers here, with sage-like advice and rude criticism from people who haven't bothered to read the question. I think it would have been better if BTS had excluded the scenario from his question and simply asked about extending the flaps above 20000', as opposed to leaving them already extended above 20000'.
Clearly there are issues to extending various various bits of metal into the airflow, versus leaving them there and that's why, for instance, there are differing speed limits for gear lowering and gear extended etc (this is only an example and I do understand the reasons behind this particular case). However, I think FlyingStone best answered the question with his quote from the FCOM:
To prevent excessive structural loads from increased Mach at higher altitude, flap extension above 20,000 feet should not be attempted.
Although it only refers to actually extending the flaps (as opposed to leaving them already extended) the FCOM is quite clear that Mach number is the problem and is, therefore, suggesting the 'excessive structural loads' will be present when the flaps are extending, as well as when they're extended, so the limitation applies to both scenarios. I say 'suggesting' because it doesn't clearly state that.
Doubtless there are those who will sarcastically say 'duh, it's obvious' but they are the same people who didn't read the question properly in the first place and consider 'extending' and 'extended' to mean the same thing.