It does depend a lot on the requirements of your team.
I have seen HR teams work with a similar culture and it worked out fine. People couldn't expect service from them outside of core hours, but in fact it turned out you just got a better coverage (someone available from 8 til 6:30).
If you're dealing with the outside world, there is generally an expectation that you can contact a company in normal office hours and someone will be there who can help. But as long as you make sure enough people have responsibility to be in during those hours, some flexibility is still workable.
Technology may be an issue. Some people simply cannot do their jobs from home, but many could that still don't.
Now, let's assume that you can technically do this. How would you sell it to management?
I would go with an approach of "You want the best people in the industry working here, right? [everyone thinks they do, even if they don't act accordingly] How better to do that than adopt a flexibility that doesn't exist elsewhere? How valuable is the ability to say 'I need to have a new fridge delivered tomorrow, can I work from home?' How valuable is the option to come in early and leave early, every now and then?"
Edit: Having reread your question, I think you're talking about a tech team in a non-tech company. In that case, the approach is slightly adjusted to "Why would the best people, who have options, come here rather than going to a technical company with a tech culture and a flexibility that our people don't enjoy? You would have to offer significantly above market rate to entice them."
In a travel company I recently worked for, I kept repeating the phrase "You're not competing with other travel companies for developers, you're competing with other tech companies," until it stuck.
Also, get the HR records, figure out how many sick days could have been saved by someone saying "Look, I've got an upset stomach, I can't be in an office today, but I can do the same job effectively at home."
Finally, working in the zone is a slightly diverse point from the rest. I would suggest that any thought-worker should be able to expect their manager to create a situation that limits interruptions. If they can't then their manager needs to understand they're not going to be as productive as they could be (which, honestly, is always an option, as long as it's understood).