How would you do this? Firstly, flow isn't really something you plan, it's more like, you get working on something and oh my god, it's 5:30 already? Where'd the day go?
Second, you can't just move meetings around, in my experience. Once something is scheduled, it calcifies; it's too much work coordinating time zones and schedules, and if you push something up, most people that were planning on it being later will be even more unprepared to discuss than usual.
This is a good point. I agree that having a 2 hour slot doesn't guarantee that I will get into a flow state, but it is a prerequisite for me to have a couple of hours at least to do this type of work.
I think the idea of being able to loosely schedule certain meetings (eg "Give me the least worst 30 minutes for the 3 people this week") could be an interesting thing to try. Having a system which knows whether it is advisable to 'bring forward' or 'push back' a meeting could be a big help. I also think that if a meeting is continually pushed back or brought forward, this might be interesting information in and of itself, especially for recurring meetings.
There could be downsides to this and I find it hard to even imagine what such a system would be like, given my current experience with Google Calendar, where even scheduling a meeting or room seems to be about 5 minute process.
Second, you can't just move meetings around, in my experience. Once something is scheduled, it calcifies; it's too much work coordinating time zones and schedules, and if you push something up, most people that were planning on it being later will be even more unprepared to discuss than usual.