How to prevent chicken from having a chalky texture?
Your temperature of 68 to 71 Celsius is very high for white meat. This is what makes the mini clumps in the breast you perceive as "chalky". If you cook it to a lower temperature, you will not have this effect, 60 to 65 Celsius makes "medium" doneness chicken meat. 

Note that food safety is a separate consideration, chicken is considered safe starting at 73 Celsius (https://www.foodsafety.gov/keep/charts/mintemp.html). So you are lowering the temperature at your own risk.