With the clay of OK you would be better off starting with mulch to cover at least 3 inches thick, 6" to a foot would be even better.
Once you have that mulch breaking down into smaller sizes then you would benefit most from adding char as you acquire it.
The decaying organic mulch materials will leak good stuff to the soil surface where it will begin to change the clay into friable soil.
The longer you simply keep the ground covered with a good, thick layer of mulch, the better the soil will become.
The terra preta discovery that started the whole biochar phenom took around 500 years to get to the point it was at when discovered.
All that means is build some soil first (char in clay isn't going to do much conditioning of the clay).
To build soil
compost and mulch along with living plant
roots are the key players, once you have a fair amount of soil with good (3-10%) Organic matter you will have
enough soil biology working to take advantage of the char.
As Phil brought up, using a tiller is not a great idea for installing(amending) char or any other amendment material for that matter, especially if you have a good supply of worms working in the ground.
If you don't have any measure of soil life now, then you might want to till in some compost for a start towards fertility but you only do that once, from then on you are working on the surface and letting the worms come and do the "digging in" for you.