Do flowers transpire?
Short answer: yes.

Floral parts, as petals and sepals, have stomata, and transpire just like a normal leaf or a primary stem (that is, a stem covered by epidermis, not periderm). And, besides stomatal transpiration, flowers have cuticular transpiration, like most of structures covered by epidermis.

This is a SE micrography of a petal's stoma:



(source: http://www.sciencephoto.com/media/32403/view)

There is a very famous experiment that we make with the kids in primary school: take a white flower and put it in a vase with coloured water. The petals will become coloured. This experiment shows that there is an ascendent flux of water, and this flux depends on transpiration. You can see it here: https://youtu.be/y9hprlmck44