Note who Flynn doesn't include as someone who he "briefed" on his call with Russia.
"Unfortunately, because of the fast pace of events, I inadvertently briefed the Vice President Elect and others with incomplete information regarding my phone calls with the Russian Ambassador. I have sincerely apologized to the president and the Vice President, and they have accepted my apology."
http://time.com/4670178/michael-flynn-resignation-transcript-letter/
He apologizes to the president (interesting he doesn't capitalize the P) and the VP for providing incomplete information to the VP. He notes that he briefed "others" but doesn't name one of the others as being the president.
Would we not surmise then that he didn't brief the president on his calls to Russia because he didn't need to as Trump already knew about the calls and the content, or because Trump never asked? Trump never asked Flynn for a month about any of this? Trump denied to the press on AF1 that he knew nothing about the reports of Flynn's calls while Flynn was actually sitting somewhere on the plane?
Flynn knows he is taking the fall for the president, but I believe he carefully worded this letter just in case.