My family member has cancer and to be around them I need my flu shot, but I refuse.
Don't you think that can be dangerous to yourself and other people?
It's my own body and no one has the right to control me
You have something against vaccines and won't get one, but in this case you could infect the cancer patient with the flu. If you refuse to get the shot then stay away from the cancer patient. If you don't get vaccinated and catch the flu you can kill the cancer patient faster by spreading your germs to them.
I want to get sick and kill my family member faster.
You should get vaccinated against the flu if it may kill your family member. You're going to hurt them and I know you said you want to get them sick, but you would feel a lot of guilt if you're the reason that they die.