The diaphragm-pulsing style of vibrato used by classical flute players has no place in traditional Irish music. Many classical flute players seem to do this automatically. It can be a really beautiful sound, but putting it in a jig or reel screams "not a traditional player" in the same way that wearing a baseball cap screams "American." So if you're a constant vibrator (to coin a phrase) you'll have to change. Blow steady, round, unwavering notes.

Vibrato is used in slow airs and other "listening" tunes, but the technique is totally different. It's derived (like a lot of the other ornamentation) from uilleann piping. The general formula is to trill on the second hole down from the note you're playing. For example, if you want to play a B with vibrato, trill on the third (A) hole, i.e. with your left ring finger. You might try other holes as well to see how they sound.

Another technique that's especially nice for high notes is to trill on the edge of the hole right below the note you're playing; for example, the second hole if you're playing a B. The good thing about this technique is that it gives you a lot of control over how wide your vibrato is - you can go from a tiny little quaver in the pitch to a really heavy wow-wow-wow sound, depending on how much of the hole you cover.

Even in slow tunes, vibrato should by no means be used all the time, or on every note. The best thing to do is to listen to how other players use it, especially pipers.