Don't get me wrong, Redcloak definitely has his own motives, but frankly I think in that comic he's convincing himself of Xykon's usefulness as much as he's convincing his underling.
But he also knows Xykon pretty well. In particular, he knows that he can pull this over on Xykon without Xykon questioning it. For his part, Xykon's usually smart enough to trust that Redcloak's strategic expertise is handy, and he's also a lich who enjoys simple joys like torturing a paladin and pitting wights against each other in gladiatorial combat. So it wasn't much of a gamble on Redcloak's part. Redcloak saw an opportunity and took it.
All that said, Xykon could kill Redcloak in a heartbeat. More importantly, Xykon could all but destroy Recloak's entire people (and Xykon seems like the sort who'd be perfectly willing to do something like that were he crossed), and Redcloak knows that. So when push comes to shove, if Xykon says, "Jump" Redcloak replies, "How high?"
So basically Xykon knows he can trust Redcloak not through loyalty but through fear, sheer intimidation, and the fact that he knows that Redcloak knows there's not a chance in the nine hells of him actually destroying or overthrowing the lich.
Redcloak hates Xykon, but is wise enough to know he's powerless to do anything about it. However, he's also wise enough to recognize an opportunity where his action might mean the difference between Xykon defeating the OotS or vice versa, and when that moment finally comes my money's on Redcloak tipping the scale in the OotS's favor.