We have a way to describe objects which “generate a blue color when light shines on them”. We say they are “blue” objects.
Likewise, bird feathers or butterfly wings which absorb/reflect light based on their small-scale structure and appear blue are still called “blue”, even though they might be colorless when pulverized.
There are plenty of “blue flowers” out there.
https://en.wikipedia.org/wiki/Blue#Pigments_and_dyes
Interestingly, the one dye listed in the link above that came from a plant is indigo, which is extracted from the green leaves of the plant https://en.wikipedia.org/wiki/Indigofera_tinctoria . There's no animal or plant I know of that both appears blue and could be used to create even a poor blue pigment, though I'd definitely be interested in any exceptions I haven't heard of.
* https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5444072/
* https://www.jstage.jst.go.jp/article/fishsci1994/61/6/61_6_9... -- see figure 2 on page 4, showing extracted carotenoproteins