Can I transfer $20,000 from the US to Australia without triggering compliance flags?

Certainly. The part of being flagged (or not), doesn’t lie in your hands and also does not lie in the amount you transfer. If there is something inherently not quite right with your transfer, you, the recipient, the nature of the transfer, the frequency, your past, your family circle, and that of the recipient, their family circle, etc. then the transaction would be flagged for a manual review.

It might be flagged, and then be on its way and you won’t even know about it. If you have nothing to worry about, go ahead. But it you are trying somehow avoid being flagged, you might succeed, or not. It just depends on your profile.