Dry measurement and conversion to weight

In general you can't convert volume measures (like cups) into mass measures (like ounces) without taking into account the specific thing you're measuring, because different substances will have different densities in a cup.

If you search online you can find conversions for different common food items but these vary. The website CookItSimply provides a conversion for cooked chopped chicken as 1 cup to 4.4oz; the website FreeFoodTips gives 5.22oz; TraditionalOven.com gives 4.94oz. Note that these are cooked weights, and chicken changes weight as it's cooked.

However, a recipe that incorporates shredded chicken isn't likely to be very sensitive to the exact quantity so I would take the recipe as just giving an indication of the rough amount of chicken to use: think of the amount that would fit in 2.5 cups and go for roughly that amount.

Conversion from volume to weight or vice-versa is different for all foods, so there is no standard rule. One cup to eight ounces only works for foods with the same density as water (it is a reasonable approximation for most liquids e.g. vinegar, milk, wine).

http://www.kingarthurflour.com/ has a printable chart of dozens of foods and weights of different amounts in ounces.