Not as clear as McDonald's website, I contacted BK directly for this information but they were not so eager to share it.
I received an email with a huge paragaph detailing how they pride themselves in being one of the first food companies to display allergen information on their website and how they must comply with a number of laws followed by one sentence saying if I needed to find out more to check the allergen PDF and this fabulous tool that filters out allergens. They obviously did not get the message that I was asking about yeast containing products or the memo that yeast allergy and intolerance is NOT one of the nationally recognised allergens so they do not need to list it.
So....the bun here will definitely have yeast. As for the patties etc...to date, who knows...
Some of the burgers contain relish that is made with vinegars. Some research suggests avoiding vinegar. I can tolerate small amounts, it may be that you can as well.