Not 100% chronological but rather the "best watching order", since "In the beginning" could have more than one place in the timeline (a 2277 Londo tells of events occuring in 2245-2248, it also spoils stuff that happens at the end of 2261 aka Season 4, which is why I put it after Season 4 where it was intended to be)
I did not include anything Crusade related, as the series was canceled before the story could be finished.
Just putting this together for personal tracking use, as sourced from this post: https://scifi.stackexchange.com/a/241222
Make sure to view by Rank for intended order.
Original description from post: The Intended Order for all TV Episodes and Movies as listed below is the order that JMS intended the show to be viewed in for full dramatic impact. This viewing order was taken from JMS's interviews, notes, and discussions. This is not a chronological order of events, and not everything is meant to make sense at first as some episodes have flashbacks and visions of things. This order (including the very similar Lurker's Guide) is popular among devoted fans.
Source 1: https://babylon5.fandom.com/wiki/Viewing_Order
Source 2: http://www.b5tv.com/showthread.php?t=11675
Note: For the Crusade spin-off the Chronological Order option is listed below as it is enjoyable and popular among devoted fans without continuity issues or jarring inconsistencies. This Crusade order is from the Babylon 5 Historical Database as authorized by JMS, with one adjustment to correct a continuity issue in "Ruling From the Tomb".
Babylon 5 Timeline
by Oktavius DeLally