Actually, it's not getting linked "canonically". No one knows how many eons have passed since the events of DS1, or how many times has the First Flame been rekindled (at least 4, but possibly a lot more) and gone out again. If you get a certain ending in DS3, you'll learn, that the Age of Dark will eventually end, too, and the First Flame can never truly go out and will light again, on it's own. So there is no "canonical ending" in DS1 (or DS2, for that matter). Especially if you take into account the fact, that Gwyndolin survives until the events of DS3, while a protagonist of DS1 may kill him, thus hinting, that DS3 happens in a different reality, than DS1.