I can’t think of any reason why that would be possible, cancer spreads as it’s cell population grows, the cells wouldn’t, as far as I’m aware, be able to be moved around with a toothbrush.
I never heard of such a risk, never read of it and never seen any guidelines in relation to such a risk.
Maybe extremely rare cases it’s a remote possibility but such rare occurrence would lie firmly in the realm of oncology not odontology.
So you would have to discuss it with a cell biologist with special interests in oncology to further explore the topic.
The benefits of continuing brushing far exceed its potential risks.
So the simple answer is no.