The prophecy of the Chosen One is a Jedi prophecy. As a Sith, Sidious has no reason to believe that it would come true in a way that favored the Jedi. He would regard it as no more than wishful thinking on the part of the Jedi. Sidious would have even less reason to believe the prophecy of the Chosen One would come true after Order 66 -- with most of the Jedi dead and the Sith in control of the Galactic Empire, the prospects don't look good for the Jedi.
Even if Sidious believed that the prophecy might be true, that doesn't mean he believed Anakin was the Chosen One. Even the Jedi didn't know if Anakin was the Chosen One or if the prophecy was being interpreted correctly:
Obi-Wan: With all due respect, Master, is [Anakin] not the Chosen One? Is he not to destroy the Sith and bring balance to the Force?
Mace Windu: So the prophecy says.
Yoda: A prophecy . . . that misread could have been.
Star Wars: Episode III Revenge of the Sith
The fact that Sidious managed to turn Anakin to the dark side would be a pretty good indication to Sidious that Anakin was not the Chosen One, even if Sidious believed the prophecy might eventually come true. After all, how could Anakin/Vader destroy the Sith if he was a Sith himself?
It's also worth noting that we do not know the exact in-universe statement made by the prophecy of the Chosen One: every mention of it is a merely a reference to it made by a character. Usually those references only mention the part about bringing balance to the Force (as in Episodes I and II) -- the "destruction of the Sith" is mentioned along with the prophecy only in Episode III (by Obi-Wan, as in the quote above). This suggests that the prophecy merely predicts that the Force would be balanced, and that the "destruction of the Sith" part was how the Jedi interpreted the prophecy. Consequently, it's possible that Sidious interpreted the prophecy as merely that the Chosen One would bring balance to the Force -- and since the Jedi vastly outnumbered the Sith, the prophecy would actually mean that the Jedi would be reduced in number (i.e. that the prophecy would favor the Sith). This is an interpretation commonly made by fans, although Lucas has said that the correct interpretation favors the Jedi and includes the destruction of the Sith.
In Legends, the Sith actually have their own version of the prophecy of the Chosen One: the prophecy of the Sith'ari. The Sith'ari is basically the Sith equivalent of the Jedi Chosen One, except that the Sith'ari would benefit the Sith over the Jedi. Sidious might have thought Anakin would become the Sith'ari instead of the Jedi Chosen One while Sidious was trying to recruit Anakin. After Anakin/Vader lost his limbs and was weakened in the Force, Sidious probably thought he would be the Sith'ari (he thought he would master the dark side of the Force and live forever).
The Legends novel Darth Plagueis provides yet another interpretation of the Jedi prophecy of the Chosen One (from Dooku) which favors the Sith. The following is a conversation between between then-Senator Palpatine and Dooku (still a member of the Jedi Order at the time), in which Dooku revealed the prophecy to Palpatine and his own interpretation of it. Because Dooku was still a Jedi, Palpatine deliberately played dumb so as not to reveal the fact that he was a Sith Lord:
“The Order’s place in this is a matter Sifo-Dyas and I have discussed endlessly,” Dooku snapped. “But the members of the Council are not similarly inclined. They are entrenched in archaic thinking, and slow to embrace change.” He paused, and adopted a sinister look. “Don’t let yourself be fooled, Palpatine. They see dark times ahead. In fact, they think of little else. That’s why they have allowed the Jedi to become involved in parochial conflicts like those at Galidraan, Yinchorr, and Baltizaar, which are like brush fires born of windblown embers from a massive blaze just beyond the horizon. But instead of actually rising up against the corruption in the Republic, perhaps disbanding the Senate entirely for a period of time, they have become fixated on prophecy. They await the coming of a prophesized redeemer who will bring balance to the Force and restore order.”
“A redeemer?” Palpatine stared at him in authentic surprise. “You’ve never alluded to this prophecy.”
“Nor would I now if I still thought of myself as loyal to the Order.”
“I never considered that the Force needed to be balanced.”
Dooku’s lip curled. “The Order interprets the prophecy to mean that the dark tide needs to be stemmed.”
“You don’t accept it?”
Dooku had an answer ready. “Here is the truth of it: the Jedi could fulfill the prophecy on their own, if they were willing to unleash the full powers of the Force.”
“The full powers of the Force,” Palpatine said. “I’m afraid you’ve lost me.”
Dooku blew out his breath. “Perhaps it’s something we can discuss in the future.”
“You’ve made your decision, then?”
Dooku nodded. “If one more Jedi dies because of indolence on the part of the Republic and moral equivocation on the part of the Council, I will leave the Temple and refuse to look back.”
Dooku rejected the Jedi Order's interpretation that "balance to the Force" meant defeat of the dark side of the Force. His position sounds suspiciously like the Sith belief that the Jedi don't use the "full powers of the Force" by rejecting the use of the dark side. The alleged "destroy the Sith" part of the prophecy is also notably absent.