From what I've read and experienced with my chickens, they don't like any citrus fruit. Maybe the question should be "will chickens eat kumquats?" instead of "can chickens eat kumquats".
Mine are pretty good at deciding what's not good for them to eat. For instance, I have a slew of mushrooms sprouting up on old stumps and in "fairy rings" in my backyard where they free range. I've read chickens love mushrooms, but not these. They won't touch them.
I agree with Ohhhdear...citrus may interfere w/ egg production but should not affect general health of chickens, from what I have read. Chickens may know what to eat or not eat, but you can't always count on them making the best decisions, nutrition wise. For example, if given the choice between appropriate feed that is balanced nutritionally or cracked corn/treats of marginal value they will pick the"goodies" most of the time! Kinda like kids, I think.
We have a few Loquat trees on our property. When we trim the trees, all the braches go into the main run for them to pick over. Our birds just love the Loquats if they are ripe. Ours will also eat grapefruit and they love oranges but they do not care for lemons.
Glad to see this question posted. I planted a loquat tree in my yard today. Then my cousin told me that her dog had gotten quite ill from eating loquats, including the pits. Had me concerned and wondering if I should replant the tree somewhere that the chickens don't have access to. Sounds like they should be okay.