I thought it was cross-contamination when you mix raw food with any food. So, can you use the same flour batter next and dip the chicken in along with French fries together and then fry them?
It is cross contamination but if you are cooking within the safe zone you are good.
It depends if you are going to keep the batter. Yes the chicken will contaminate the batter but if you are throwing out the batter then OK. Save the batter in fridge for even a day and use is not a risk I would take.
One concern could be taste carry over. If you do the fries first there would be very little taste transfer. Even chicken first would not be much taste transfer.