Why do most disposable lighters have two chambers of fluid?  Is that
little bar down the middle just for added structural integrity, or do
the multiple chambers have an effect on the way the gas is fed into
the ignition mechanism?

I think it is largely a structural thing
- but it does have a functional effect

Because there are two chambers, with a little jiggling one can halve
the wasted gas when the lighter is 'empty'.

Not much use to me as the flints invariably wear out first.