My guess is that 1/2” for movement at each side will be sufficient, as much of
the movement of individual boards will be accounted for by adjustments at the
individual tongues and grooves. Is the edge boards actually moved a full 1/2”,
that would be more than the nails could easily accommodate.

My personal choice of whether to install the floor under the shelves would
depend upon the construction of the shelves. When I did something similar, but
much smaller scale, at a previous residence, i built the shelf to have the face
of the toe kick installed after the shelf unit was secured.  I installed the
shelf first, ran the flooring to where the baseboard would cover it, and then
scribed the baseboard to fit tight to the flooring.  The appearance is
indistinguishable from installing the flooring first.   You could also do it
with a baseboard and a shoe molding or quarter round, but I personally prefer to
scribe the base to the floor over using a shoe mold.

David Sobel