1. Babylon 5: The Gathering
Set in 2257, same as your link.
2. Babylon 5: Season 1
Set in 2258, same as your link.
There's a more convoluted approach to Season 1 that re-sorts the episode order based on production order, script details, and a few other factors, but practically speaking there's not really any compelling reason to approach it in any order other than what's on the DVDs.
3. Babylon 5: Season 2
Set in 2259, same as your link.
If you want to get into 'expanded universe' media (much of which is actually JMS canon), there are a number of novels and comics that slot into Season 2, but for the 'lay person,' just the episodes in the DVD order is perfectly fine.
4. Babylon 5: Season 3
Set in 2260, same as your link.
Babylon 5: Season 4, Episodes 1-8/9
Babylon 5: Thirdspace
Babylon 5: Season 4, Episode 9
All set in 2261. Thirdspace is...a nuisance. To be completely nitpicky, I think it fits in most accurately if you play episode 409 for the first few minutes, pause it, watch Thirdspace, then go back to 409. But even that doesn't make complete sense (not to mention it's a really onerous thing to ask of someone coming into the series for the first time). So I'd say your link's placement of it between 408 and 409 is probably the simplest compromise.
6. Babylon 5: Season 4, Episodes 10-22
Also set in 2261, same as your link.
There's an argument that 422 should be either moved to the very end and act as a coda to the entire story (which I don't like simply because it feels like it undercuts everything else), or else dropped entirely (which I also don't like, because I dislike skipping anything). Again, for simplicity's sake, it's probably easiest to just watch it as the last episode of Season 4.
7. Babylon 5: Season 5, Episodes 1-21
All set in 2262, same as your link.
8. Babylon 5: The River of Souls
Set in 2263, same as your link.
9. Babylon 5: The Legend of the Rangers
Set in 2265, same as your link. (But oh my god is it ever awful)
This is where your link says to put "the rest of season 5" (ie: 522 Sleeping in Light). That cannot be the case, as Sheridan meets his destiny in 522, but is still around in Call to Arms, Crusade, and Lost Tales, which are later in your link's order.
10. Babylon 5: A Call to Arms
Set at end of 2266, same as your link. Again, Sheridan appears here.
Set in 2267, same as your link. There's no end to the debate about which order to watch these episodes in.
12. Babylon 5: The Lost Tales
Set in 2271, same as your link. Again, Sheridan appears here.
13. Babylon 5: In the Beginning
So this is the difference of opinion one. Your link wants this right after Season 4, and I cannot figure out why. If the flowchart's author wanted it to echo War Without End, that was in the second half of Season 3 (so why wait till end of Season 4 to watch it?). Alternatively, the framing story for this (Emperor Londo) is set in 2278, long after the events of the main series and Crusade.
My thought is to put it here, right near the end, for a couple of reasons. First, it brings the whole franchise's story full circle by revisiting the origin story of what got us started, and how that dictated all the years of story between then and now. Second, it ties off the recurring time-travel thread that first appeared in Season 1, came back in Season 3, and now here we finally see it in its final contemporary context--with the benefit now of knowing the whole story. Third, it gives us the opportunity to revisit Londo and G'Kar one last time (for G'Kar it's the first time we've seen him since Legend of the Rangers, 13 years earlier; for Londo, the first time since B5 Season 5, 18 years earlier). It also gives the two characters their final exit, making it unequivocally clear why neither appear in "Sleeping in Light" (and bonus points for making the lines in SiL about absent friends feel more acutely melancholic than they do without recent context).
As an added bonus for people interested in checking out the (canon!) expanded universe, here may also be a good spot to check out the (JMS canon) Legions of Fire novels, which detail the nearly two decades that Centauri Prime was secretly occupied and Londo himself controlled by the Drakh. The author of the trilogy gets almost all of his dates wrong, but still manages to tell the great tragedy of the Centauri in a compelling and depressing way, and that trilogy ends shortly after the conclusion of In the Beginning.
14. Babylon 5: Season 5, Episode 22
The final ending, set in 2281. Aside from it naturally falling at the end due to its being the latest date in the franchise (minus Deconstruction of Falling Stars), I think that Sleeping in Light is just the perfect period at the end of the sentence for this universe. It's very much the end for us viewing the story, and the end of an era in-universe as well. I can't fathom anything else wrapping this universe up.