I can only really explain from my personal experience as I’m no vet, but it seems that quite a lot of bull terriers are allergic to chicken specifically. In theory, a dog could be allergic to any foodstuff — it just seems that chicken crops up an awful lot in this particular breed. My boy Badger has always had issues with dry, patchy skin, though at one point it seemed to suddenly worsen quite dramatically; bald patches started to form, with small scabbed lumps (they looked similar to some kind of insect bite - in fact, we thought it may have been sand flies to start with! You can see examples here and here [not my dogs - this is Lorraine Sheppard of Polanca BT’s dog Poppy]) which didn’t seem to heal. These patches occurred around the top of his head (just between his ears), his lower back, ribs, and hind legs. Daisy, being on the same diet, didn’t react as significantly — though she did lose the fur on the base of her tail and the skin became extremely dry. We tried all sorts of antibiotics prescribed to us by the vets, and none of it worked - it was only until a good friend and breeder of bullies for over thirty years asked if we fed our dogs any form of chicken-based products that bells started ringing. Some say it’s what goes into the meat when it’s processed that causes the skin to react, but this breed is known to be prone to dietary-based illness regardless. I know a lot of bull terrier owners that feed their dogs raw chicken wings and have had no trouble whatsoever — but after everything we’ve experienced I’d honestly have to suggest trying any kind of new food with bullies on a trial basis. If any allergies occur, switch them back onto a food you know is suitable for them! Grains also seem to be another problem - I’m not saying cut them (or chicken, for that matter) out of your dog’s diet completely, just to be aware that reactions do unfortunately happen so it’d be best to keep a careful eye out.
If your dog does develop a rash similar to what I’ve described, I would also be very wary of the advice your vet may give you as it’s almost certain they’d prescribe long-term antibiotics — which generally help for a while but tend to eventually aggravate many skin conditions. Go to your vets by all means - just be aware of the consequences antibiotics may have on your dogs overall health! Alternatively to medicating your bullie, there are a few things you can do; changing the diet is probably the first thing to do if any symptoms develop, though if that doesn’t work and the problems show no signs of clearing, try some natural neem seed oil diluted in a carrier oil (I’ve used tea tree and jojoba) at a 1:10 ratio dabbed onto the affected areas. Tried it on Badger as a last resort after a friend recommended it and it was the only thing that cleared it up - keep a bottle in at all times now just in case!
There are a lot of things you need to consider before getting a bullie - they’re not the easiest of breeds to own and you really need to assess they’re really the right breed for you! So many times in rescue I’ve seen first-time bull terrier owners get bogged down by a variety of things (stubbornness, boisterousness, and the sheer strength of the breed are usually the biggest factors) through no fault of their own (they aren’t for everyone - and there is no shame in accepting that!) and turn their dog in for rehoming. I’d really advise reading this for some all round insight!
It is true they are prone to certain illnesses - the major players being deafness and blindness in white dogs, as well as skin conditions, renal failure, joint issues (usually caused by either genetic conditions or the dog developing too quickly) and heart problems. However — responsible breeders will have tested for all of these things (excepting skin conditions, but we’ll get to that in a wee minute) in the parents, so if you’re thinking of getting a puppy make certain to ask to see the parents’ test results before making any decisions! I have to admit that Daisy was a puppy who came from a friend - a trusted friend, mind - so we cut corners a little. 6 months down the line she was diagnosed with the genetic disease craniomandibular osteopathy - a rare illness in bull breeds, admittedly, but it’s a reminder that you should always research your new puppy thoroughly! Skin problems in bull terriers can be recurring and costly depending on the severity - for example, demodex mange is prevalent in the breed and can be another expensive and stressful illness - not just for you, but your dog also. I’ve also seen dogs ( my Badger included!) who are incredibly sensitive to certain foods that cause them to get bald, blistered patches - I’d avoid feeding a bullie chicken, if I’m honest, as I’ve heard many stories of it being detrimental to skin conditions!
Another major thing to consider is the overall personality of the breed. They are wonderful, beautiful dogs to have in your life — but they’re also little sods that will make you want to tear your hair out on occasion! Of course, every dog is different, but the base characteristics of the breed will always be there. If you want a dog to obey you instantly, to sit at home all day, to live in a perfectly decorated house without incident, or even one to look fierce outside your home.. well, you’re in the wrong place entirely. They’re intelligent to the point of being sly, though their stubbornness often tricks people into thinking otherwise - they will test your patience constantly! Training is easy and hard at the same time - they understand things very quickly, but trying to convince them into doing it is a different kettle of fish. They never grow up, either - they will often be puppies right up until they die, so you have to be prepared to accept this part of their nature.
I hope you understand that this is not intended to put you off of getting a bull terrier - they are an amazing breed of dog ( the only one for me!) and if you can be the steady, patient (and yet playful) owner that they need they will genuinely change your lives for the better. They’re incredibly empathetic, loving dogs who will wholly loyal to their humans and to other animal friends if raised with them — but you need to be absolutely sure that they’re right for you before you commit to sharing your home with one of these magnificent pig-dogs.