The http://www.uesp.net/wiki/Books:The_Daggerfall_Chronicles. Is this considered a canon source? I mean, it has a lot of information about the background, characters, lineages etc. Most importantly (to me) it states that Helseth was born 3E 376,
Morgiah was born 3E 384 and that Barenziah was born in 2E 893. This... can't be right? Well the Barenziah date anyway.

My problem with this date is that she would have been only three years old at the signing of The Armistice Treaty (Morrowind's surrender to Tiber Septim). I was always under the impression that it was at this time that Barenziah and Tiber had their... get together.

So is the Daggerfall Chronicles, which is just the "Official Strategy Guide" for The Elder Scrolls II: Daggerfall a canon source as far as dates and information go? Or has Barenziah's birth date just been retconned?

Yup, it is. Like with anything older, there are some things which have since been contradicted, but, as a whole, it's a good source of information.

The dates do line up with what we know about Barenziah from other books. She was shipped off to Skyrim before the Armistice, spent a while first at court and then in the streets, and only later was found by the Emperor's men and taken to the capital.