After watching the crisis episodes, IMO I guess you have to definitely watch Arrow and maybe Flash and Supergirl.
ARROW: (Important to watch)
The final season deals with the build-up to the crisis event and also throughout the season hints at
the death of Arrow in the crisis.
It also explains more about the crisis' effects and about the Monitor and so this season of Arrow is important
FLASH: (Not important)
The latest season of the Flash also deals with the prophecy that:
The Flash WILL DIE
However, frankly there isn't much in the season about crisis that hinders your viewing. The only plot-point that aligns with the crisis is the introduction of Nash Wells who believes Monitor is a false god and unknowingly starts the crisis
Supergirl: (Not important for crisis. Important if you want to avoid spoilers for season 4)
Well supergirl is the "my opinion" part since I have not watched the show after the Elseworld crossover and was going to continue it... And so I was hit with these spoilers while watching Crisis
- Lex Luthor DIED (When was he introduced?)
- Lena Luthor knows about Kara/Supergirl? And apparently she hates both the Danvers sisters
- Some woman was having the Guardian shield
- Legends of Tomorrow: No need (unless you want to know about the romance novel that Mick reads to the baby...) [as of the 3rd crisis episode]
- Batwoman: No need [as of the 3rd crisis episode]. Basically the Supergirl-Batwoman friendship continues from the Elseworld crossover. There are some spoilers regarding:
Her sister? killing her parents or something?
Depends on your current Batwoman watching trend. If you started the show, might as well finish it...
- Black Lightning: No need [as of the 3rd crisis episode]
- Arrow is necessary (For background related to the crisis)
- Supergirl is necessary if you want to avoid spoilers for season 4
- Flash and the other shows are not so necessary