With the caveat that this is not really a programming issue as pointed out in the comments, unless, of course, you are planning to build the player into an app or webpage..., you may find that a frame accurate player would meet your needs - there are many of these available including browser based players - e.g.:
Some of these will allow you seek to an SMTPTE timestamp down to hundreds of a second which is better granularity than most video frame rates anyway.
On that last point, its worth being aware that for any common video codec there will not be a different frame per millisecond timestamp also - you are limited by the frame rate of the video itself.
For example, imagine you wanted to display the frame at exactly 10 seconds and 400 milliseconds and your video frame rate was 30 frames per second.
Every frame after the 10 second point (assuming it has a frame at exactlythe start of the 10 second point and each frame is 33 ms long for simplicity) would take 33 milliseconds, so at 10 seconds and 400 milliseconds you would be showing the 12th frame and you would actually see the same frame from 10 seconds and 396 milliseconds through to 10 seconds and 429 milliseconds.
This may not matter in your use case, but if your chosen player can seek to frame and not time then you can seek by frame numbre after calculating the nearest frame(s) from the time. This does assume a constant frame rate but that is most common at this time.
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