Now, most people I've seen on the internet don't seem to get what Dissidia's story's about, or in what order the cutscenes should go in to help it make sense.
Therefore, for your convieniance, I am making chronological videos showing the story progression. I've currently got up to video three, and I'll update this post with more videos as I make them.
Note: this wouldn't have been possible to do without Squall_of_SeeD's game script, avaliable here: GameFAQs: Dissidia: Final Fantasy (PSP) Game Script by Squall_of_SeeD
Chronological Videos
Dissidia Final Fantasy Chronological Storyline, Part 1
Dissidia Final Fantasy Chronological Storyline, Part 2
Dissidia Final Fantasy Chronological Storyline, Part 3
Dissidia Final Fantasy Chronological Storyline, Part 4
Dissidia Final Fantasy Chronological Storyline, Part 5
Dissidia Final Fantasy Chronological Storyline, Part 6
Dissidia Final Fantasy Chronological Storyline, Part 7
Dissidia Final Fantasy Chronological Storyline, Part 8
Dissidia Final Fantasy Chronological Storyline, Part 9
Dissidia Final Fantasy Chronological Storyline, Part 10
Dissidia Final Fantasy Chronological Storyline, Part 11
Dissidia Final Fantasy Chronological Storyline, Part 12
Dissidia Final Fantasy Chronological Storyline, Part 13
Dissidia Final Fantasy Chronological Storyline, Part 14
Dissidia Final Fantasy Chronological Storyline, Part 15
Dissidia Final Fantasy Chronological Storyline, Part 16
Dissidia Final Fantasy Chronological Storyline, Part 17
Dissidia Final Fantasy Chronological Storyline, Part 18
Dissidia Final Fantasy Chronological Storyline, Part 19
Dissidia Final Fantasy Chronological Storyline, Part 20
Dissidia Final Fantasy Chronological Storyline, Part 21
Dissidia Final Fantasy Chronological Storyline, Part 22