Someone told me the other day when I asked why not use AP flour for more flakiness, "Bread Flour has a higher gluten content which gives it more body. The thing that makes it flakier is putting in a lot of oil, kneading it for like 8 to 10 min, and letting it rise for 24 hours on the counter in an oiled bowl with a dishcloth covering it."
"BREAD FLOUR?! Hey man, are you trollin'?! "
There's three things that you're taking into play here.
First, there's the Bread Flour, which many of us have already confirmed is too high in gluten for deep dish.
All Purpose Flour (or an industry blend, sometimes described as Pizza Flour or 00 "Double Zero") is the flour to use.
I like Heckers/Ceresota because it has been around since the mid to late 1800s and it is my suspicion that there weren't a lot of flour options back in Chicago in the 1940s. http://heckersceresota.com/
Second, kneading develops more gluten and gluten is the enemy of deep dish crust
Over-kneading deep dish dough can create too much gluten, which makes dough stretchy, and can lead to chewy, possibly bread-like crust.
We're not making NY style, so chewy is not the goal.
If the dough is OVER-over-kneaded (8 to 10 minutes sounds like over-over-kneading to me),
it can start to break the gluten strands that had developed from initial kneading,
and then you're more likely to end up with crumbly, rather than tender and/or flaky crust.
That may be the texture you're going for. Everyone has a different preference.
TheKitchn.com has an article about over-kneading and under-kneading:http://www.thekitchn.com/bread-baking-clinic-under-knea-157484
Third, oil is the thing that helps the tender
part of the equation.
Tom Lehman has an article about what oil does for pizza dough: http://www.pizzatoday.com/industry-news/oils-affect-dough/
You want to combine the ingredients, and then knead just long enough for the dough to get a minimum amount of gluten to shape into a relatively smooth ball, so it can rise properly. The oil will also help keep the moisture in the dough to help with the rising.