If a person ear trains pitches of piano will he be automatically able to understand the pitches of flute or should he do some extra ear train for flute ? For example can we say if a person ear trains for piano he will have to work another 25% to ear train for flute ? Or is it 0 %?
Flute and piano have quite different timbres related to their overtone spectrum. In particular, flute has quite fewer harmonics, a much less pronounced attack and a continuous tone.
To put this in some anecdotal perspective: when mixed choirs are singing in unison, it is quite usual that male voices are singing one octave lower than female voices. Now I happen to be a male alto and I've heard from several of my female co-singers that it was seriously confusing to them to have me singing at their pitch because of the different timbre.
So the most important detraction is that you might need some additional effort getting the octave right. Also your pitch detection might be somewhat trained to latch onto a composition of overtones that just isn't there with a flute.
It's not as much that you'll need additional ear training rather than getting your existing skills aligned to the timbre of the flute.
Of course the good news is that additional other instruments will be much easier to accommodate once your pitch detection skills are not exclusively trained on piano cues, something that is known as "overfitting" in the context of neural networks, matching the training data set in more than the essential categories you actually want to be detecting.
I teach ear training to kids and what I do is I ask them to sing melodic intervals. I don't even play the piano. I want them to use their own voice. After all voice is our instrument. If you can sing it you can hear it. Sometimes there are students who can't sing in tune but they can recognize the intervals when I play a musical dictation. -so don't be discouraged if you can't sing it perfectly. They have learned already minor thirds, major seconds, perfect fiths, major chords. Ascending and descending. and now I'm teaching them to map it out to to other regions. You start with the penthatonic scale intervals and once you have this you add the half steps. Since ear training is about pitch, not timbre, I don't think you will have any problem translating that into the flute sound. Just adjusting to it.
Piano is really good instrument to start ear training with since the pitch does not change easily so it is a really good tools to teach the sense of absolute pitch - I do not like the word "perfect pitch".
However, it is a terrible teaching tool to train ear in long term because it has temperament problem. It is tuned to equal temperament and world does not work that way. It is not natural and does not work very well with other instruments including flute.
This seems a very minor problem, but it could created a big problem if it is ignored for a long time.
I think it is equally important to teach both absolute sense of pitch and relative sense of pitch. My choice is to start with piano because absolute sense is more difficult to acquire since it is not natural. But before things go too far, I would add training with voice or stringed instrument. Flute is also a very good one to add. I will add more of relative ear training moving on. However, aural skill improves along with the knowledge of music theory. At one point, ear training needs to turn into aural training and include theory.