The short answer on that crispy skin
Skip the skin for your dog, even though it smells irresistible and crunches in a way dogs love. The plain meat underneath a rotisserie chicken is a very different food from the skin that covers it. Skin is where the fat renders and collects during cooking, and on a shop-bought or home-roasted rotisserie bird it is also where the salt and seasoning rub sits. A dog who gets a torn-off strip is not getting a taste of chicken so much as a concentrated bite of fat and seasoning, and that is the part most likely to cause trouble.
That does not mean the family meal has to exclude your dog entirely. A small amount of plain, cooked chicken meat, taken from the breast before sauces are added and checked carefully for bones, is the shareable part. Think of the skin as yours and the unseasoned meat as the dog-safe compromise.
Why skin causes more problems than meat
Fat is the first issue. A sudden rich load can bring vomiting a few hours later, soft greasy stools the next morning and a hunched, uncomfortable dog who skips the next meal. Dogs who have had pancreas irritation before, dogs carrying extra weight and very small dogs given a strip sized for a person are the ones most likely to struggle.
Seasoning is the second issue. Rotisserie rubs commonly include onion and garlic powders, smoked spices and a lot of salt, none of which belong in a dog's bowl. You cannot rinse that seasoning away reliably because it has cooked into the fat. Bones are the third issue when skin is pulled off carelessly: rib slivers and small cooked bones tear away with the skin, and cooked bones splinter rather than soften, so any shared piece needs a careful finger check first.
What to offer from the same bird instead
Wait until the bird has rested, then cut a modest piece of breast or thigh meat away from any skin, gristle or bone. Remove every trace of skin from that piece, keep it plain with no gravy or stuffing clinging to it, and cut it into bites suited to your dog's size. For a small dog that might be a few pea-sized shreds over the usual dinner; for a large dog, a palm-sized amount mixed through the bowl is plenty. Treat it as part of the day's food, not an extra meal on top, and reduce the regular portion slightly if you are sharing generously.
Serve it in the bowl, not from the table. Handing skin or meat scraps from plates teaches pestering and makes it hard for children or guests to know what is allowed. A clear household rule, meat yes in the bowl and skin never, prevents the hopeful stare from being rewarded by different people in different ways.
Signs to watch after a skin slip-up
If your dog has already stolen or been given skin, watch the rest of the day calmly rather than assuming disaster. A single small piece in a healthy adult dog often passes with nothing worse than a loose stool. Offer water, keep the next meal plain and modest, and let the stomach settle.
Contact your vet promptly if vomiting repeats, your dog refuses food and seems painful or restless, or stools become watery or bloody, and call at once if a puppy, a small dog or a dog with past digestive trouble ate a large amount. Describe how much was eaten and whether bones may have gone with it, because that detail changes the advice you will be given.
Keeping the rule straight at family meals
The hardest part of the rotisserie question is rarely the nutrition and usually the table full of people making their own decisions. When sitters or relatives feed your dog on other evenings, that same no-skin, plain-meat-only note is exactly the kind of detail worth writing down once in KinsLe Care Teams, so every helper works from the same feeding instructions.