Given the exact phrasing of the original limitation, I think the question was a reasonable one and did not deserve the offhand comments it has received.
There are plenty of aircraft systems which can have multiple limits on some types, like landing gear: one maximum for deployment, one for when it's down and yet another for retraction. Also can be IAS, mach or both.
On the 777, the computers won't let you deploy flap >20K which can be problematic if you have a certain type of static failure and the aeroplane still thinks it's at 30,000' even though you're nearly on the ground.
I'd guess there are sound aerodynamic/structural reasons why it isn't a good idea to fly around at high altitude with flaps/slats out, so Boeing have thought what might be needed for operational reasons (going in/out of Bogata, for instance), added a margin then rounded it up to 20,000'. The text doesn't say what exact configuration, so there would logically be less of a problem with F1 than F30.
It's one of those scenarios that rewards a little previous thought. Like BOAC, I don't regard 20K as a hard "wings stay on/wings come off" limit but would be reticent to exceed this unless it was to avoid something worse, like hitting a mountain or running out of fuel.
The answer to: "Can you climb above 20,000 feet with Flaps extended?" would be yes, of course, but only if you *really* need to. It takes quite a bit of imagination to get to that point but hey, you never know.
Also, "If I lose an engine below Vmcg can I attempt a takeoff anyway?", could be answered by yes as well. Not all attempts will be successful, depending on the exact circumstances! It's not something that's recommended either.
(Next time in the sim in a twin, try a single-engined takeoff from stationary - surprising what a non-event it can be...)