That depends. Most cats with an allergy to chicken can take Dr. Jones' Ultimate Feline Health Formula. Usually, I find that cats 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 Feline Health Formula does contain chicken, but it is in a small amount, so most cats with chicken allergies should be able to take it.
In short:
Yes, your cat should take Dr. Jones' Ultimate Feline Health Formula even if they have a mild allergy to chicken.
If your cat is very sensitive to chicken - if he/she reacts to even a small amount of chicken - then No, do not give Dr. Jones' Ultimate Feline Health Formula to your cat.