Having now been on Mt. Kilauea and seeing real live flowing lava (though still never having seen magma flows) I can say that a magma flood should be quick, but jerky.
Visibly what happens is the liquid rock flows very quickly, but upon contact with air/water it cools down quite fast. This causes the surface to cool and slow. Soon it stops, but pressure from the remaining liquid rock builds behind it and causes the warm rock to bulge then crack, from there more liquid rock flows just as fast as before. It's a cycle. Above ground, in contact with air, you would never see a whole line of pure liquid rock. It cools too fast and would form a barrier of cooler rock above it.
Also, from studying the volcanic rocks and petroglyphs out here, I've noticed that magma is mostly iron, sulphur, and various other porous rocks. If a lava/magma flow contacts certain rocks like limestone, it burns that rock off, though if it's cool enough it could become instead encrusted with limestone forming a light or white rock exterior. Never do you see obsidian as a result from cooled lava.
Also, while it's feasable to find a lava tube that is only half full, it's not common, and usually means that the lava source is running dry. This may not happen though for another 30-80 years. I have even gotten to walk through a lava tube myself. You can see how there were different levels of magma over different points in time by how the tube formed. What this means is the magma river should ebb over the course of the years, maybe taking as many as 100 years to finally disappate. Of course this would have to be tied in with volcanic and techtonic activity too, so might never make it in.
Just thought I'd post my findings here in case Toady wants to make the subteranean activities of the mountain a little more realistic.