How to play a piano or any instrument with emotion/good flow?

Firstly, you practise a lot to get the technicalities and fluency nailed. Then, you've to feel what the composer may be trying to convey through the score, and bring across those to the listeners through your performance. Sometimes these feelings come naturally, but sometimes you've to use your head to figure it out and decide on the best way to present it. An overflow of emotion isn't good, especially if you're playing in front of others (well if you're just recording it and playing for yourself, it doesn't matter so much because you're likely to be comfortable with what you hear). Overdone emotions make audiences cringe because they see all these grimaces on your face, even when the music doesn't call for them. 'Feelings' for pieces come more naturally to some people than to others (those who can intuitively feel the composer's intentions are usually very sensitive and musical by nature), but everyone can learn to put some emotion into their playing if they're taught properly and work hard enough at analysing pieces. Different harmonies have different 'colours' and moods, and with a trained ear, you'll be able to pick up on those clues. A trained ear comes with practice and analysing different music intelligently (meaning, not just 'this sounds good but I don't know why'). Same goes for how the composer writes the music - texture, melody, accompaniment, articulation, etc. You definitely need some sort of musical training to unscramble all that and get to the core of the music. It isn't terribly hard though, so by all means go for it. It can only help you.

Play the violin. Use a lot of vibrato and legato. For anything, play it like it is your LIFE. Anything less is not as beautifully emotional. Not that I'm supporting emotions.

You need to master the technical aspects of the instrument first.

** Emotion: it is best to let the music speak for itself, and whatever you have to add to it yourself will simply come through in your performance. Anything else would be an imposition.

**Good flow: a matter of good musicianship. As long as you are not a total klutz, everything will come out quite nicely.

It is surprising how much of this is taken care of by technical polish. The rest is up to the individual, and that 'rest' is not part of a "How To...." It belongs to the domain of artists, and somehow artists speak Greek, it seems.....except to other artists who understand perfectly. It is very mysterious.
(Arrrrggh !!!)

Practise, practise and practise until playing the instrument becomes as natural to you as breathing.
Then the music will flow from you as if you were speaking.