1-5 and 13 are canonically in the same timeline, 4 being the first (5 being in the middle of 4), several hundred years pass then 1 begins, a year later is 2, then 3.
7 is a prequel to 6 (think Eliwood and Roy for reference), and is largely hinted at being in the same universe as 1-5+13 but no canon confirmation that I'm aware of.
8 is by itself, again, no canon correlation to the others.
9 and 10 follow a three year gap between each other and is largely implied at being the beginning of the series, but no confirmation of being tied to the other games.
11, 12, and 15 are remakes of 1, 3, and 2 respectively.
14 is sometime before Awakening, but given the way space, time, and outrealms work it could very well be technically in the future of Awakening yet somehow before 4-5 or 9-10. It's a mystery, especially considering the lack of lore behind it.
Also the entirety is thrown for a loop because of outrealms from 13 and 14.