I can see from Eliza’s link what a “flat white” looks like, but I’m not clear on the reason it’s called “flat”.  Is it because the foamed (I assume) milk mostly floats on the surface?

Yeah, double-double is a Tim Horton’s thing, but other coffee shops here will know what it is if you order it.

What do you get if you order a toil-and-trouble?

Percolated: fire burn and coffee bubble.

Edit on flat white from Wikipedia:

Derek Townsend, the co-owner of DKD café[5] in Auckland, New Zealand, claims to have developed it, though acknowledges that the term “flat white” was already in use in Sydney to describe a similar style of coffee.[6]

And from this dedicated coffee site about its origins and the probable reason for the term:

Coffee lovers say the term “flat white” emerged in cities such as Sydney and Wellington in the late 1980s and early 1990s. Where it originated is hotly debated.

Paul Bassett, a lead player in exporting Australian coffee techniques and styles to Japan and South Korea says that the ‘march of the Flat White’ is part of a backlash against cappuccino - people just don’t want all that foam any more.