By the time your chicken and brisket are done. All the bacteria in both the chicken and the brisket will have been killed, period. The only thing you have to worry about are the toxins that were produced in the chicken by the live bacteria before they were killed by the heat.
I don't believe that the amount of bacteria toxins falling on the brisket from the chicken are going to amount to a hill of beans. I'd eat the brisket without a second thought.
My feeling is that once the meat is placed in temps over 220f there is going to be very little bacteria activity going on. Most of the bacteria will be on the outer layers of the chicken and the beef and will be killed first as the heat moves from the outer layers into the center of the meat.
Most of us worry about the bacteria making us sick but really it is only the toxins that are left behind in the meat that are a danger to us after the meat reaches 140f and above. .
The real error here is that The poultry should have been cooked at a much higher temperature than brisket is. I'd worry more about eating the Chicken that was done at too low a temperature than eating the brisket
Ergo, I do not do Chicken and Beef in the same smoker.