I wonder what "flunkey" means in this context?
"There he had an opportunity of refreshing
himself with both the bottles at once, looking out at a low
blinding wall three feet off, and speculating on the number of
Barnacle families within the bills of mortality who lived in such
hutches of their own free flunkey choice.

I don't know, wwh. This one's a hard one. Here's MW on it:

Etymology: Scots, of unknown origin
1 a : a liveried servant b : one performing menial or miscellaneous duties
2 : YES-MAN

The Barnacle family here live in apparently less-than-ideal houses. The Barnacles in the novel really do live as a cluster of barnacles, one offspring following the footsteps of another, passing on a heritage being of self-important civil servants.

However, flunkeys were often referred to as liveried servants, but that's not the case here with the Barnacles whose own liveried servants were less than impressive. I'd read the passage to suggest that their flunkey choice was the choice of one given to performing menial duties, not hard work or chores, but here the menial duties of the civil servant.