It's hard to find any info on chickens grazing scotch broom. I read the BC council write up and yeah, it's annoying when there are no references given for each statement in a publication.
I did find this tidbit from :
https://wiki.bugwood.org/Cytisus_scoparius#BIOLOGICAL_CONTROL
Chickens, surprisingly enough, are known to effectively digest (and destroy) all weed seeds passing through their crops and they can thoroughly graze back vegetation in areas up to one acre in size. Releasing chickens into an area after the mature plants are removed allows them to scratch and peck out weed seeds and potentially reduce the weed seed bank in the soil (Andres 1979).
which references this 1979 paper : Andres, L.A. 1979. Biological control will it solve the broom problem? Fremontia 7(3):9-11.
I couldn't find the 1979 article
online, but you may be able to have a librarian at your public library or nearby university library find it for you.
So it sounds like the biological control the chickens would provide is more from scratching seedlings than actually eating the seeds. The above quote specifically says "weed seeds" which leads me to believe the 1979 paper is about general control of all weeds using chickens.
Scotch broom seems to be toxic to chickens in large amounts.
Poisoning from this shrub is usually of a mild type. Large amounts are required to
cause symptoms in animals. Alkaloids have been identified as being the toxic principle.
from page 19:
https://ssl.acesag.auburn.edu/pubs/docs/A/ANR-0975/ANR-0975-archive.pdf
So I would say it's not a good candidate for use as chicken
feed, but chickens may be used to control scotch broom provided they have access to other food sources to prevent overdose.