First of all there's no "I have to" when it comes to the fandom worlds and that is one of many things that is awesome. And secondly, this is my own personal opinion and doesn't have to apply to everyone.
I can tell you right now that there is at least 2 Arrow episodes that will confuse the fuck out of you if you do not watch The Flash. Because when they say it's crossover, dude they fucking mean it. Part 1 of 2 is in Arrow/The Flash and they have part 2 in the other show. And they start where they left off like it was the same show it started in. Confusing? It can be until you watch it but believe me those 2 crossover episodes are even more confusing because I remember sitting there being like "Did I miss an episode?!".
Moving on to Legends of Tomorrow. I suppose it can be a bit confusing if you haven't watched Arrow or The Flash, mostly The Flash, since many of the characters are introduced in those shows. If you on the other hand, like me, have grown up with DC comics then you already know them and it's less confusing.
So my answer to the question?
If you want the full badass experience then yes, you'll need to watch all of them.
But if you for example only want to watch Arrow and can handle the extreme confusion
when those crossover episodes come on then no.
But I do recommend them all from my very heart. I highly enjoy all of them and I'm extremely happy that someone finally was brave enough to hop on the crossover train and they are doing an AMAZING job too. Marvel may be dominating the movie world but DC is dominating the shit out of the TV world.
Also I know this post gets a little bit confusing here and there but I didn't want to give you any examples on the story line. Because everyone don't know most of everything when it comes to comics. And I do my best to keep this blog spoiler free so I'm sorry haha! Just ask if something confused you to the point where your brain broke! :)
Do you follow any of these shows?
Or all of them? What's your opinion?