Yes, there are multiple methods of intel-gathering. One method is to capture people, torture and question them, and learn something new that way. The other method is to send spies.
The first method has some major disadvantages - people will say anything when they are in pain, including things that are obviously not true. So, sure, someone might confess to their part in the Kinslaying...but how would you even know that there really was a kinslaying at all? It might be all made up. Some of the 'confessions' torture has historically wrung out of people are clearly nonsense. I'm saying that the Noldor are as likely to confess to witchcraft or child rape as to the kinslaying, and presumably those first two aren't really happening, so...the questioners need to know what questions to ask.
The issue with spying is that you have to be around people who will talk about the secrets. The Noldor all know about the Kinslaying and have little reason to discuss it. They may make some oblique references to it, but it's not like they're going to sit down and start reminiscing about it in any detail. So, a spy would have to actively prod someone into talking about it, by pretending to already know what is being discussed. And...well, that's difficult to do. The doppleganger/shapeshifter effect can help, as Sauron could go sit down with Caranthir while looking like one of his brothers and just ask him things. But...it's not like Celegorm would have any reason to say, 'so, brother, tell me about what happened when we left Valinor' so it's still a challenge to write a spy scene that gains any knowledge of the kinslaying. You need to know what you're fishing for....
Here's what the Villains already know:
1) Morgoth knows about the Darkening of Valinor and the Death of Finwë and the theft of the silmarils....because he did all of that himself
2) They know that the Noldor came to Middle Earth in two 'batches' - that some came in Teleri ships (which they burned) and some crossed the Helcaraxë.
3) They know that it's *just* the Noldor, no other elves and not the Valar....but....Thorondor is around, so maybe hold the phone on the 'not the Valar' bit. Maybe the Valar are just being sneaky or delaying for some reason? Hard to say.
4) They know about the unrest of the Noldor, and the feud between Fëanor and Fingolfin. (Again, because Morgoth directly caused that himself.)
So...the villains know that there is a story in why the Noldor came to Middle Earth separately (some following Fëanor, some following Fingolfin), but they *don't* know about what happened at Alqualondë.
I think we should have some Sindar question the gaps in the Noldor story, and that would be a good way for the Villains to figure out that there are questions to be asked here. Through some combination of questioning captives and spying, Sauron learns of the Kinslaying. It's just...how, exactly?