I think you don't need to have deep flow state to make progress at work.
For me I think flow state is more about how interested I am about the task than how much time I have. And frankly many tasks at work aren't that interesting so even if I have half of day uninterrupted time, I don't get into flow state.
Entering a flow state is a combination of multiple things IMO.
The amount of challenge needs to be challenging enough for your skill level, not too easy (boring) or not too hard (can't flow because you get stuck).
And (at least for me) I need to have the knowledge that I can focus on the task and not be interrupted. If I have a meeting in 30 minutes, there's exactly zero chance I'll enter a flow state because I'm expecting the meeting to start. And if I accidentally enter flow, I either work past the meeting or my flow is interrupted by a calendar alarm.
Interruptions during flow state are really damaging (for me) because I'm juggling a huge amount of context and data in my head that's not yet exported to any external medium. If I get interrupted a large-ish segment of that data will disappear and I need to spend time gathering it after the interruption has passed.
