Height varies by breed and individuals.. Some may be near three feet, others close to four (no joke, very rare but is possible.) Again, the same thing goes for the roost. This varies by breed and individuals, breeds like games and Sumatras don't have a problem flying up 6, 8, 10, 15 feet in the air.. While a heavier breed like a Sussex may only be able to fly 4-6' (I don't know for sure, not spent any time with Sussex.. Just saying.)
Also you need to take into account weight, like my Shamo's being such large birds (two of my cocks are somewhere between 9 and 11 pounds.) it isn't suggested you put a roost higher than 2, maybe 3 feet off the ground or it can damage their hock joints. And they are also poor flyers, I have seen my largest bird jump about 5 feet in the air but he doesn't fly long or high like the American birds which can fly 15-20 feet probably for a good 60-70 feet (if not more..)
I watched my bantam Old English hen fly straight up into the air about 10 feet and fly an easy 30-40 feet.
I have rather largeish sussexes (by north american standards anyways, they would not hold a candle to anything in the UK!).
They are just, you know, chicken-sized
I would not give them less than 18" over the roost if you can possibly avoid it, especially if you have a rooster (they need to stretch *up* to crow). They can squish into just 12" or so of headroom but not enjoyably and if you live somewhere that gets cold winters you may have condensate/frostbite problems with their heads so close to the ceiling/wall.
In an A-frame ark you really don't have a lot of choice, of course... I suppose it's too late to talk you out of that design as you've already made it, but it really doesn't provide very good quality living accommodations, mysteriously-popular though it is in British backyards.
If it were me, I would err on the side of putting the roost lower (even if barely above the bedding to give them more headroom, rather than raising the roost with the result that they have *both* not much headroom *and* the roost is constantly in their way when they are trying to walk around in there. With the low roost you may have some trouble iwth them sleeping in the nestboxes instead of on the roost but frankly that is just an unavoidable hazard of most A-frame type designs and you should probably just accept that fact and not owrry about it when deciding how to locate the roost.
Then there's the location of the vents to consider. You don't want to put the roost right next to a vent that will be left open in cold weather, because that's going to set up the perfect conditions for a cold draft (bad).
Ah, well that is a bit different! LOL It might be worth putting that in your profile so it is displayed under your name so you don't have to keep reminding people every time you post, which you are otherwise likely to have to do
In Hawaii you *can* get away with minimal indoor space (as long as they have shade and shelter from rain, depending on where on your island you are), I would still suggest trying to have at least 14" of clearance above the roost and preferably more if you have a rooster, though.
Good luck, have fun, totally jealous of your climate