I think it might be safe to assume that "Rocks" might be that "lurking legend" that Oda mentioned at Jump Festa.
That quote went on to state that the Straw Hats would fight their "greatest enemy ever, who might be related to Whitebeard", so if we assume both lines refer to the same person/group then Rocks might have some type of connection.
The Ace novels (which are canon) confirmed that Kaido is from the same generation as Shanks and Big Mom is from the same generation as Whitebeard and Roger (but didn't become as prominent as she is until after), so I'm a bit skeptical about them having been crew mates. That being said, Big Mom's line about "getting along like the good old days" seems to imply that their crews were at least allied at some point between the aftermath of Roger's death and Luffy starting his journey (maybe they had a similar relationship to the Strawhats and Firetank pirates where they collaborated for a common goal and weren't on particularly bad terms but weren't exactly a package deal either).
That being said I don't think that it's impossible that Kaido and Big Mom were members of "Rocks" together (Assuming that "Rocks" is a pirate crew, not an individual).
We don't know how old Kaido is, but he appears to be middle aged (maybe late 50s at oldest, assuming he isn't a hybrid member of Oars' race with a ridiculous lifespan), and if "Rocks" was defeated by the Marines 40 years ago Kaido would potentially had to have been in it as a child. However, the fact that there was a bit of a gap between "Rocks" and Kaido coming to power doesn't really add up to me. I doubt that Kaido would just lay low and not do much for an extended period of time. I feel like he would have immediately made a name for himself.
That line about "Rocks" growing stronger despite losing its captain initially brought Shiki to mind, but I doubt he was involved in it, since he was arrested years after when "Rocks" was in their prime. Ever since Oda began dropping hints about Kaido's involvement in Wano at the beginning of Dressrosa I've had a feeling that he was a member of the Golden Lion Pirates in his youth due to a number of parallels between the two (Both are explicitly shown to be influenced by Japanese culture in their designs and have japanese names, Kaido's plan to create a zoan army seems like a better version of Shiki's plan to create an army of animals, and having a Yonko from the GL pirates would cause the current generation to mirror Roger's 1 to 1)
Idk though, maybe the timeline could be something like this:
-Linlin joins Rocks in her mid-to-late 20s
-Kaido (potentially) joins Rocks as a child/teenager (depending on how old he is, assuming he was in Rocks)
-Linlin captains the Big Mom pirates
-Kaido (potentially) joins the Golden Lion pirates as a teenager (depending on how old he is, assuming he was in the GL pirates)
-Kaido forms the Beasts/Animal Kingdom Pirates
-Big Mom and Kaido begin rising to power
Another interesting thing to note: if Kaido was in "Rocks", maybe some of those various defeats/surrenders that were mentioned when he was introduced happened while he was a part of that crew.