This is already sort of possible for particular moves (if you need to check out some particular ones) by using our API - see Is there a way to see how long you took for a move when reviewing a game - #4 by Lys for details.
It is not readily avilable in our UI yet and there is also trouble with interfacing it with the .sgf format and download as sgf only currently supports “time left on clock” NOT “time spent on a move”, which can be confusing all of which is a complicated way of me saying - the funcionality is almost there so if anyone is interested in helping making it “real” check out our github and consider contactig eugene as I think he was doing something in that area