I've had the same experience as @Ithaca. I was surprised when Dr. G said flow is not possible while practicing. Mihaly Csikszentmihalyi is one of my favorite psychologists. I've read most of his books. Here's a cool diagram:
Csikszentmihalyi describes the flow state as the experiential space where high skill level meets high challenge level, resulting in a particular state of mind (strange movement of time, wellbeing/euphoria). To qualify as a flow activity, it must have a well-defined goal, specific actions, and immediate feedback. If skill and challenge aren't in balance, you get into some other mental state. For instance, I lose time bingeing a favorite show on Netflix but there's no skill to it, and when I wake up from my binge covered in Cheeto dust, I'm definitely not feeling euphoria.
But when I was in the Army, I was a highly skilled translator, and I could sit at my station transcribing radio transmissions all day, rocking the flow state, suffused with a tremendous feeling of wellbeing. I was doing what I was trained to do, and, as the transliterated Russian filled up the page in front of me, not easily but skillfully, I felt great. But one day, they had us work in full protective (MOPP) gear, including gas masks. Wearing MOPP gear wrecked the balance between my skill and the difficulty level of the activity, and THAT was a LONG, GRUMPY DAY.
I don't get into the flow state every time I sit down at the piano, but when I'm equal to the challenge of what I've decided to do, time flies, and I feel great for the rest of the day. I can get into the flow state while cooking, cleaning, making art, crafting, or any number of things. But what I've noticed is mindset is very important to maintaining the state of flow. I loved making art so much that I decided to quit my job and build an art studio in my house. But after that, it was a real challenge to get into flow and stay there. I kept pushing the challenge level too high, both in terms of technique and emotional challenge.
So I wonder if making music your job, or putting too much financial and/or emotional pressure/challenge on it, disturbs the balance between challenge and skill. I have zero to lose with piano, and everything to gain, because I never intend to make money doing it. I can modulate the challenge perfectly to meet my skill. I fall out of flow when I push myself into music that's too hard for me, or when the piece is too easy, I can get bored. So I'm not convinced it's a matter of "no one can ever get into a flow state while practicing," but it's very much individual with respect to the balance between skill and challenge while you practice.