Reading your post I just wonder if it's more a fear about dying than a fear specifically about cancer?
I also wondered if a fear of dying might be what's beneath the surface anxiety over cancer - once I read your mention of severe food allergies. My dd10 has multiple life-threatening food allergies, and she's had some scary reactions. FWIW, the age around 5-6 years old was the time that anxiety over allergic reactions and fear over them really ramped up. I don't have any great advice re how to deal with that, but wanted to let you know that it later ramped down in a *huge* way once dd had been through the first few years of elementary school.
Anyway, might be totally off-point, but just thought I'd mention it!
polarbear