In general, cold and room temperature food need more seasonning as the volatile compounds that make up odor (what you smell) will not be as, erm, volatile.
There is not set rule on how much to add; experience plays a big role here.
When cooking your ingredients, in your case, chicken, you can add a little bit more seasoning, herbs, spices, salt.
Just be careful not to add too much as some herbs and spices can become bitter in larger quantity.
For your specific case, I would add cilantro and lime to the wraps.
(In my taste, ) I would skip the carrots and cucumber as they are not that flavorful and add water to the end product; make a side salad with them.