I'm not sure you are talking about the same thing when you say "flow" that I think most of the other people are talking about when they say "flow".
Flow as most are using it here, also known as being "in the zone", is when you achieve a deep state of focus on one particular task, and everything else seems to melt away. You reach maximal energy and enthusiasm for the work. It is where you reach peak productivity and creativity.
Most people cannot just enter this state at will, and when they do achieve it cannot maintain it for more than an hour or two. Getting into this state takes 20 to 30 minutes or more.
When you are in this state it takes very little to knock you out of it. A ringing phone, someone talking to you even if you just tell them to come back in a couple hours, a beep from a messaging app...all of those can knock you out of the zone.
Getting back in after being knocked out takes another 20 to 30 minutes. This means that if you are getting one interruption or distraction every 30 minutes throughout your time at your desk it is unlikely that you will get any time in the zone.
>> In the same vein, an office with a door won't help at all if you have higher-ups who expects instant responses to any messaging/e-mail query every five minutes
> Well, if you don't answer instantly, then you are stopping them in their flow
In the case of a manager interrupting you they probably weren't in the zone. But even if it is someone who was in the zone that is interrupting you them having to stop and message you was probably enough to knock them out of it.
It will almost certainly be more productive for the organization overall for them to work on something else until you naturally exit the zone.