Yes,
Burrenton Forge-Tender's ability can prevent damage dealt by
Stormbreath Dragon. The Dragon's protection from white means exactly four things: any damage that a white source would deal to it is prevented, it cannot be enchanted or equipped by anything white, it cannot be blocked by a white creature, and it cannot be targeted by white spells or abilities from white sources.
Burrenton Forge-Tender's ability doesn't use the word “target”, so it doesn't target anything, and it's definitely not attempting to do any of the other three, so protection doesn't hinder it in any way.
On a side note, as you probably noticed this forum isn't a good place to ask when you're interested in receiving quick confirmations or clarifications. Instead, we're focused on providing definitive answers to rules questions in situations where the answer to those questions are potentially relevant to (and possibly unknown by) a significant portion of the judge population, especially when other reliable sources may disagree or where the associated rules are themselves unclear or incomplete.
For straightforward questions about how things work, there's a wide variety of other sources to choose from, such as the
#mtgrules chat room or the dedicated Rules areas on the larger Magic forum sites, many of which will provide answers that are just as correct and informative, usually far faster than you'll receive them here. These more open venues often have multiple people available specifically to answer whatever questions might happen to be asked at all hours of the day.