Actually, did you know the Flute is called the
OCARINA in the A Link To The Past Japanese Version, Triforce Of The Gods.
This is the Artwork Of The Ocarina in A Link To The Past, the only Minor difference is that there is no Triforce Symbol around the Mouth Piece.
Also!!!! The Minish Cap uses this same utility as in A Link To The Past, as the Minish Cap features The Ocarina Of Wind.
Again, Minus The Triforce Symbol around the Mouth Piece.
With The Ocarina Of Time, it does have the ability to Warp you around, but only if you are at Triforce Crest Platform, otherwise, it's useless when it comes down to Warping; And also the Ocarina does not feature a Big Bird Picking you up and taking you to different locations.
I would definitely have to say, the Ocarina from The Minish Cap, and A Link To The Past, definitely have Relation, but as far as the Ocarina Of Time, meh .. they have some relation. Appearance wise yes, but as far as the Ocarina demonstrated, not so much. However, Majora's Mask demonstrated that is Possible, that are related, because it does features you playing the Ocarina Of Time to make a Bird take you around different locations, when you play the Song Of Soaring to call out The Owl in MM.