Trump was too smart to get black mailed. That’s what makes him so deadly to the deep state. Trump and Putin have a common enemy - the Deep State/Shadow Government/Cabal, or whatever you want to call it, who are trying to play the two off of each other. Putin understands this.
Trump’s lawyer, early in his career, was a man named Roy Cohn, a suspicious, some would say paranoid, man. Trump spoke highly of him. It seems likely that he helped Trump to figure out how to operate in the cut throat business world in which he operated, without being compromised by unscrupulous politicians and businessmen. It also helps that, throughout Trump’s career he has been willing to own up to any of his personal indiscretions. It’s hard to blackmail someone for having an affair if he’s willing to acknowledge it publicly.
In short, Trump is too smart to have allowed himself to be compromised by Putin. Besides which, there is no will on the part of Putin to do so.