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Any animal can get cancer, you just don't hear about it as much in non-pet species. In fact, chickens are extremely prone to reproductive cancers and are even being used to research ovarian cancer and cancer-fighting diets. I have a friend who is doing research into diet and the effects on cancer using chickens. They slaughtered 50 birds, the oldest of them being 5 years old, and every single one of them had one kind of cancer or another! They did ultrasounds on them before slaughtering and necropsies on them after to determine the type and incidence of cancer.
As for telling in a hen that's still alive, I'm not sure how you would do that without a vet visit. I know at my vet, the first test to determine if a mass is possibly cancerous is to do a fine needle aspirate and look at what kind of cells are present under a microscope. We also detect a lot of cancers using x-rays, and some using ultrasounds (although ultrasound is generally used to confirm a mass rather than diagnose it at my vet). And some masses you can actually feel just by palpating the abdomen (although there is no way to say definitively whether they are cancer just by feeling).