We are in a severe drought so everything is struggling. Would we be
wise to pinch the flower buds and give the plant an opportunity to use
its energy to get established?

Why not make sure it gets enough water?

Good parts of zone 7 (at least here in Washington, DC) have been
having the kind of hot dry weather which tests even that strategy.
The plants lose so much water through the leaves that they can
sometimes droop even if the soil is moist (although if this is their
only problem they'll tend to perk up at night). Soaker hoses (not
watering cans) a must if you hope for "enough" water. High water
bills. Possibility of leaching nutrients out of the soil from
overwatering. Time consuming to do all that watering, move hoses,
etc. And so on.

Pretty common this time of year, but worse than usual this year.

Personally, I'm more of the "plant something which can cope with the
usual summer drought" philosophy. But for weather this bad, and new
transplants, I'll make at least a partial exception.

So going back to the Clematis, I don't Clematis too well, but pinching
the flower bud of new plants (a) can't hurt the plant, in terms of
getting established, (b) defers the gratification of flowers
(obviously), (c) is something I've never really consistently had the
patience for. So I guess I'm not much help on this one :-).