I have both the June McCormack books & CD’s which are pretty good.
I’ve heard good reviews of the Conal O Grada tutor but prefer June McCormack’s style of playing, I’ve not heard of the Fintan Vallely tutor before - they’re all very good players.
An alternative is the OAIM - http://oaim.ie/ where you can sign up for some useful free video lessons some of which are on Youtube all downloadable.
The six (free) Steph Geremia videos would be good for a beginner see below -
Conal O’Grada’s book is excellent, especially the section on close listening which is probably 80 percent of the process of learning to play Irish music on the flute. All the technique in the world won’t help if you’re not a careful listener, and a good chunk of his book is focused on that.
There’s also Grey Larsen’s Essential Guide to Irish Flute and Tin Whistle, which is full of good info and might be especially helpful for people coming to Irish music from other genres; it includes a few pages on Irish music on Boehm-system flute, for example.
Conal O’Grada’s is brilliant. I’d pick that one first. June McCormack’s is very nice for learning tunes with good style. Grey Larsen’s is well written and thorough, but it’s almost too encyclopedic in its scope. It could lead to information overload. And I have some quibbles with some of the approach to ornamentation: I’m not a fan of his fingering system, for instance.
I highly, highly suggest signing up for a subscription with the Online Academy of Irish Music. They have hundreds of very well done whistle and flute lessons from some of the most respected players in the world. http://www.oaim.ie