If I were you I would immediately change to the Fromm Beef Frittata. You are currently feeding the chicken and it's amazing how many bullies are allergic to chicken. So before you go through the whole thing of switching to a different food then I would try the beef and see if it is not just the fact that you are using chicken that is the problem!!
You also have a lot of bulldogs who are allergic to grain ... so if it's the grain that's giving him the itchies and not the chicken then you are still choosing a good flvour to switch to, because you're covering both things! Beef frittata is grain-free ... Chicken is not.
The Fromm Beef and the Fromm chicken are both in the 4* range .... that means you don't have to do any type of gradual switch. You can switch immediately because the Fromm 4* range is interchangeable. There's nothing stopping you from feeding beef in the morning and then a totally different flavour in the evening.
Hope that helps .... trying the Beef is the first step in my opinion