Your dog could have anything from lactose intolerance to food allergies, to a touch of a gastrointestinal bug (stomach virus), to inflammatory bowel disease (IBD).
Keep a food diary and try to determine if there is a correlation between something that she has eaten and vomiting. It can take up to 12 hours or more for her to show symptoms. So something that she has eaten the day before could also be the culprit. If it does turn out to be the milk, she may have lactose intolerance or a dairy allergy. Dogs can develop food sensitivities or food allergies anytime in their lives to any food, even something like chicken, if they are allergy prone.
If the problem becomes more frequent it may require investigation by your veterinarian. A food trial may be warranted. This consists of feeding a hypoallergenic food for 8 weeks and nothing else during that period of time. If the vomiting stops than it can be assumed that she was allergic to something in her previous diet. This could be the milk, the Cheerios, chicken, or any ingredient in her old dog food. Under veterinary supervision one ingredient at a time will then be added back to her diet. If no adverse reactions occur within one week of giving the test food it can be assumed that she is not allergic to the food.
Lastly, over the counter Children's Zantac or Pepcid can be given occasionally to calm the stomach. Pepcid dose is 1 to 2 mg once daily. Zantac dose is 5 to 10mg once daily.
I think you should stop giveing her chiken and milk thats what i would do