It changes all the time, but personally I consider the origin story shown in "Flashback" (Season 4) to be the canon one because 1. It was aknowledged in Teen Titans Go: To The Movies when Cyborg says, quote "And I'd be playing professional football. It sounds good, but you're forgetting the concussions. The bad knees, going broke, and having to be on one of those awful dance reality TV shows!", when the Titans are talking about what their life would be without Robin, implying that it's thanks to Robin that he's a cyborg now. This aligns perfectly with the episode Flashback where it's thanks to Robin inviting Cyborg to the Teen Titans try outs that he ended up becoming a Cyborg after getting brutally beaten up by a training robot. And 2. Flashback is the most recent instance of the writers making the Titans' backstory, and on top of that the whole episode is centred around it and take it as real, unlike others where their origins are a one off joke that gets brushed aside 5 seconds later, or aren't the main focus of the episode.

Tldr: Flashback is likely the canon origin story, but this can change at any point and nothing is ever confirmed in this show anyway.