That depends. Most dogs with an allergy to chicken can take Dr. Jones' Ultimate Canine Health Formula. Usually, I find that dogs with a chicken allergy are not acutely sensitive to chicken - most only have a reaction if their daily food contains chicken. In other words, if they have a diet with chicken as the primary protein source, they have an allergic reaction. Dr. Jones' Ultimate Canine Health Formula does contain chicken, but it is in a small amount, so most dogs with chicken allergies should be able to take it.
In short:
Yes, your dog should take Dr. Jones' Ultimate Canine Health Formula even if they have a mild allergy to chicken.
If your dog is very sensitive to chicken - if he/she reacts to even a small amount of chicken - then No, do not give Dr. Jones' Ultimate Canine Health Formula to your dog.