Both the Beard and I have recommended all of the Arrowverse shows, so when someone asked me if the order you watch the Arrowverse shows matters while I was drinking my apple juice, well I spewed my drink all over my questioner. It was not pretty. After apologizing profusely, I exclaimed, “Of course, it matters!” She avoids my phone calls, now to my chagrin, but I completely understand. We geeks can be a bit manic.
Again because I’m manic, I’ve tried to make it neat and understandable. If it is neither of those things, or unclear in any way please comment. Also, you will find a bit of shorthand here. Arrow 1.01 means Arrow Season 1, Episode 1. This is the third post of the continuity so I’m starting where we left off, which would be after Arrow Season 6, Flash Season 4, Supergirl Season 3, Legends Season 3, Black Lightning Season 1. Also, because Black Lightning is not immediately part of the continuity, I leave Season 2 until the end of Arrow’s seventh Season, but will include him in Season 8. Be patient and all will be made clear. Without further ado my craziness on display.

The Arrowverse Continuity: An Obsessive Compulsive Point of View (Part III)
Flash 5.01 to Supergirl 4.01 to Arrow 7.01 to Flash 5.02
Supergirl 4.02 to Arrow 7.02 to Legends 4.01 to Flash 5.03
Supergirl 4.03 to Arrow 7.03 to Legends 4.02 to Flash 5.04
Supergirl 4.04 to Arrow 7.04 to Legends 4.03 to Supergirl 4.05
Arrow 7.05 to Legends 4.04 to Flash 5.05 to Supergirl 4.06
Arrow 7.06 to Legends 4.05 to Flash 5.06 to Supergirl 4.07
Arrow 7.07 to Legends 4.06 to Flash 5.07 to Supergirl 4.08
Arrow 7.08 to Legends 4.07 to Flash 5.08 (Elseworlds Crossover Begins)

Flash 5.09 to Arrow 7.09 to Supergirl 4.09 to Legends 4.08
Flash 5.10 to Arrow 7.10 to Supergirl 4.10 to Flash 5.11
Supergirl 4.11 to Arrow 7.11 to Flash 5.12 to Arrow 7.12
Flash 5.13 to Arrow 7.13 to Flash 5.14 to Supergirl 4.12
Supergirl 4.13 to Arrow 7.14 to Flash 5.15 to Supergirl 4.14
Arrow 7.15 to Flash 5.16 to Supergirl 4.15 to Arrow 7.16
Flash 5.17 to Supergirl 4.16 to Arrow 7.17 to Supergirl 4.17
Legends 4.09 to Legends 4.10 to Arrow 7.18 to Legends 4.11
Flash 5.18 to Supergirl 4.18 to Arrow 7.19 to Legends 4.12
Flash 5.19 to Supergirl 4.19 to Arrow 7.20 to Legends 4.13
Flash 5.20 to Supergirl 4.20 to Arrow 7.21 to Legends 4.14
Flash 5.21 to Supergirl 4.21 to Arrow 7.22 to Legends 4.15
Flash 5.22 to Supergirl 4.22 to Legends 4.16
I suggest now that you watch all of Black Lightning Season 2, because in Season 3, Black Lightning becomes a part of the Arrowverse continuity and Batwoman gets her own title. (Batwoman is currently available on the cwtv.com website for free.)

Batwoman 1.01 to Supergirl 5.01 to Lightning 3.01 to Flash 6.01
Batwoman 1.02 to Supergirl 5.02 to Lightning 3.02 to Flash 6.02
Arrow 8.01 to Batwoman 1.03 to Supergirl 5.03 to Lightning 3.03
Flash 6.03 to Arrow 8.02 to Batwoman 1.04 to Supergirl 5.04
Lightning 3.04 to Flash 6.04 to Arrow 8.03 to Batwoman 1.05
Supergirl 5.05 to Flash 6.05 to Arrow 8.04 to Batwoman 1.06
Supergirl 5.06 to Lightning 3.05 to Batwoman 1.07 to Supergirl 5.07
Lightning 3.06 to Flash 6.06 to Arrow 8.05 to Lightning 3.07
Flash 6.07 to Arrow 8.06 to Batwoman 1.08 to Supergirl 5.08
Lightning 3.08 to Lightning 3.09 to Flash 6.08 to Arrow 8.07
(Crisis on Infinite Earths Mega-Crossover Event Begins)

Supergirl 5.09 to Batwoman 1.09 to Flash 6.09 to Arrow 8.08 to Legends 5.01
Batwoman 1.10 to Supergirl 5.10 to Lightning 3.10 to Arrow 8.09
Legends 5.02 to Batwoman 1.11 to Supergirl 5.11 to Lightning 3.11
Arrow 8.10 to Lightning 3.12 to Flash 6.10 to Legends 5.03
Lightning 3.13 to Flash 6.11 to Legends 5.04 to Batwoman 1.12
Supergirl 5.12 to Flash 6.12 to Legends 5.05 to Batwoman 1.13
Supergirl 5.13 to Lightning 3.14 to Flash 6.13 to Legends 5.06
Lightning 3.15 to Batwoman 1.14 to Supergirl 5.14 to Lightning 3.16
Flash 6.14 to Legends 5.07 to Batwoman 1.15 to Supergirl 5.15
Flash 6.15 to Legends 5.08 to Batwoman 1.16 to Supergirl 5.16
Flash 6.16 to Legends 5.09 to Batwoman 1.17 to Flash 6.17
Legends 5.10 to Batwoman 1.18 to Supergirl 5.17 to Flash 6.18
Legends 5.11 to Batwoman 1.19 to Supergirl 5.18 to Flash 6.19
Legends 5.12 to Batwoman 1.20 to Supergirl – 5.19 to Legends 5.13

All right, I think that it should be understood that this year the Arrowverse shows ended abruptly, because of the Corona Virus. There were more episodes scheduled, and once shooting halted, there was a disagreement as to how to proceed. I don’t know if this contributed to Ruby Rose’s departure from Batwoman, but I don’t think it helped. Legends Season 5 is not yet available on Netflix but you can definitely watch it on the cwtv.com website.
I believe that the continuity, such as it is, is more or less correct, but if anyone has suggestions as to how it may be improved, I’m willing to listen. Since the shows will not return until 2021, that leaves us plenty of time to re-watch these shows. Check them out in the order I’ve delineated over the course of these three weeks and let me know what you think. Godspeed, and please, stay safe.