Most hams get RF burns from direct contact with the antenna or indirect contact through their transmitter because the antenna was unbalanced and their gear wasn’t properly grounded. It is not quite the same thing as a radiation burn.
Radiation burns usually happen because someone was too close to an open waveguide while the transmitter was running. Once the energy is coupled in to the antenna, it usually becomes so diffuse that it isn’t a problem. The primary cases where this might be of some concern is when you put a walki-talky close to your face or place a smart-phone close to your head. In those cases you may be approaching the lower limits of the FCC’s radiation guidelines. There may also be a few extreme cases with close proximity to high power radar systems or climbing around cellular telephone cell site antennas.
However, these ratings have a fudge-factor built in to them. The only documented medical damage cases I have heard of were due to cataracts in the eyes at levels above 10 mW/meter² for a sustained period of time (minutes).
Remember, this is only thermal energy. There is no ionizing component to this, so it is very unlikely you’d get cancer. If anything, the localized heating may actually help to kill cancer cells. If you’d like to read the gory technical details, see the FCC’s OET 65 document.