Hi John,
I recommend that you start off by using the synthesizer source. It's monophonic and it's more distinguishable in the faster delays. I somehow reached level 44 in this game, and the best advice I can offer is to listen to the filtering effect and take note of how much separation you can hear in each sound. Once you listen enough times, it will still be really hard to guess the exact ms, but it will be a lot easier to guess which ms it is not. Try this: close your eyes and listen and try to guess the ms. Before choosing the answer, open your eyes and see which answer is closer to your guess, pick that answer. Trust your gut feeling, this game is a mixture of mainly instinct and luck. The end goal is to do well consistently every time based on skill, which I believe will happen over time.

Try to listen to the sound texture. The delay time itself is hard to notice with very short delays, but the sound texture is different. Good luck!

Thanks guys. I've been listening to the texture, but I still haven't figured out the textural difference between say, 3ms and 20ms. Seems I'm getting it right on the basis of chance at the moment.

3ms vs 20ms is very hard to decide, but i think, if you hear carefully, you will notice that the 20ms maybe sounds a little bit "wider" than the 3ms.

Do you think that a 'practice mode' can help?

Depends on how it works. The longer times are relatively easy, at least in the sense that you can figure it out by counting the seconds. But anything under 50ms is really hard. So would love a practice game where you can choose to only practice certain MS (eg. everything under 50ms) or some ideas on what the difference is between 5ms, 10ms, and 20ms, etc.

An "adaptive" or "progressive" mode could help. You start with a long delay that is easy to spot and progressively reduce the time while you still answer correctly. When you answer wrongly, you return to a longer one and the refinement progress starts again.
Maybe these examples can help to get the ideas:
https://en.wikipedia.org/wiki/Computerized_adaptive_testing
http://jakemandell.com/adaptivepitch/