This would be like playing with radioactive material. The NY Times knows the identity(-ies) of the author(s). For this to be a false flag by Trump, this would require faking a dissent from inside the White House, writing a letter, and going to the NY Times to get it published through a person that says they are against the Leader of the administration they work for.
But it's not impossible. I didn't want to bring it up, but I'm glad someone else did. While it's not likely, it's plausible given what Republicans have done. They ginned up false evidence to go to war with Iraq. Projecting what they do onto political opponents and gaslighting the nation has been routine practice since 2000 when the Presidency was stolen from Al Gore by a conservative SCOTUS. They unlawfully denied Obama his final SCOTUS pick. There willingness to completely subvert the law in order to gain and/or maintain power is well documented. Etc.
So why would a false flag operation be so out of the question?
Conservatives hate the free press, and they make little effort to state otherwise. If, for example, this was used to declare some kind of state of emergency wherein certain Constitutional protections were suspended, which could include shutting down media outlets, the NYT would be completely silenced and its staff likely arrested. Thus, the person(s) behind the letter would actually benefit, rather than be harmed by this.
Yes, that's a very dark, even paranoid scenario, but it's within the realm of possibility.
Republicans either face defeat in November, or finding some other way to hold onto power. They've done everything else, so why not this step?