Gaurahari
Nitya, flute is for krna's vrindavan lila not even for mathura lila.

Lord Jagannatha in our home ALWAYS has a flute and it is in his LEFT hand.

I started doing this since I read the translation of :
Jagannathastaka
(As issued from the mouth of Lord Caitanya)

Verse 2:
bhuje savye venum Shirasi Shikhi-puccham katitate
dukulam netrante sahacara-kataksham vidadhate
sada shrimad-vrindavana-vasati-lila-paricayo
jagannathah svami nayana-patha-gami bhavatu me

"In His left hand Lord Jagannatha holds a flute. On His head He wears the feathers of peacocks and on His hips He wears fine yellow silken cloth. Out of the corners of His eyes He bestows sidelong glances upon His loving devotees and He always reveals Himself through His pastimes in His divine abode of Vrindavana. May that Jagannatha Svami be the object of my vision."


Since this is coming direct from the Lotus lips of Lord Caitanya himself - I think we can all clearly say that this is the highest Authority on the matter.

ys
Radhesyam dd