Aaron,
You pose a really good question, so just wanted to make sure you got a response, although certainly plenty of advice in that previous thread. This is my own take on things and everyone is different, but I think this mirrors the path for a lot of other people who play traditional Irish music.
There’s two basic things to practice - the mechanics and the music. The mechanics are certainly important (getting a good tone, dexterity across the flute, working on crisp ornamentation, etc.) but all of those things can be improved with repetition and practice. I believe there are some older threads where people have suggested various exercises for all of this. At the same time, there are a lot of great players who just work on this by playing tunes, so choose your own adventure.
The harder part is learning to play the music. There are lots of ways to do this but it basically comes down to listening to good music, whether that’s in person or over recordings. In my opinion, it’s really important to learn tunes by ear (at speed and slowed down if necessary) when you do this. This is about more than just learning the tune. It’s about developing an educated/critical ear for listening to the music.
If you are practicing at home, I’d encourage you to pick recordings of players you enjoy and sit down with them when you practice and go through the tunes. Make sure you listen to more than just flute players. By doing this, you’ll start to pull out what you like about a specific player - how they emphasize the rhythm, the setting of the tune, the variations they play, etc.
You can even take a tune or a standard set of tunes and listen to different versions to see how different players approach it. For example, you could learn a lot just by taking the Tarbolton set, starting off with Coleman, and going through various recordings of it over the years from different players.
Ultimately, you want to build up all the good qualities in your own playing that you appreciate in other people’s playing and make it your own. By listening to other players, you also are better able to listen to other musicians when you are playing with them and have a conversation by hearing what they are doing with the tune.
Then, to quote Seamus Ennis, you have the whole lot, only to keep on practicing it.
Hope that helps,
Brendan