There is a range of things one can do after realizing an Answer you've posted has an error. In the short run one might self-delete the Answer, to give yourself a chance to "find the flaw". Having self-deleted your Answer, it is usually a simple matter to undelete it on your own decision after a suitable edit "behind the scenes".
It may be that the flaw can be quickly found and corrected. This is very common, and I would venture it has happened to everyone who has posted several dozen Answers. But your Question here seems to be directed at the case where you realize the Answer is wrong but cannot find the flaw, much less quickly correct it.
A minimum step would be to add an acknowledgement at the beginning of the post that the Answer that follows is wrong. It should be explained (in a brief way) why you know the Answer is wrong, and this could be accompanied by a summary of the other correct Answers on the Question.
You should not in most cases start a new thread to ask Readers to find the flaw in your Answer. Such a request, if you feel it sensible, can be incorporated in the notice of wrong Answer described above. In rare cases I can imagine that a mistake (or the inability to spot the mistake) would inspire a new Question, but this is not the first step towards rectifying a known error in an Answer.