He was regarded as a master piper and a global ambassador for traditional Irish music.
O’Flynn was born in Kildare in 1945 to a musical family.
He gravitated towards the uilleann pipes and by 11 he was taking classes with the renowned Leo Rowsome.
He formed Planxty alongside Moore, Lunny and Irvine and they became an influential and innovative group.
They toured extensively and O’Flynn was able to bring his skill with the uilleann pipes to a worldwide audience.
Planxty broke up in the mid 1980s, but O’Flynn’s career continued to flourish playing with several famous musicians, including Kate Bush, Emmy Lou Harris and Mark Knopfler.
He also worked with composer Shaun Davey on the Brendan Voyage.
His expertise was extensive and he worked with orchestras, on film soundtracks and with poet Seamus Heaney.
The Arts Council has expressed its regret at the passing of O’Flynn.
Chair of the Arts Council Sheila Pratschke said: “Liam O’Flynn has left behind him an incredible legacy of music through his recordings, his careful support of other musicians and artists and his dedication to transmission of the great heritage of Irish music to future generations.”
Ms Pratchske said he had a huge influence on the artistic life of Ireland and was well known for his artistic collaborations with artists from other traditions and practices.
By Sinéad Crowley Arts and Media Correspondent