When does ginger flower?

When growing ginger as outlined above you won't see any flowers. A clump needs to be about two years old to flower. So if you want to see your ginger flower leave it in the ground, and just dig very carefully at the edges of it to harvest bits here and there.
The flowers of culinary ginger are green and insignificant anyway.
There are however some spectacular flowering gingers. If you are after great flowers get some of those. They are grown exactly like the culinary ginger, just skip the harvest :-).
There's also a pretty variegated ginger, with white and green striped leaves. All the ornamental varieties are evergreen in the tropics (meaning they don't die down like the culinary ginger).