I agree with David that, if you are going to amend soil for trees, you have to think about drainage first.
DO NOT DO THIS:
Just dig a planting hole in the clay , amend it, and plant.
Any rain would fill that amended hole, displace all the air, drain VERY slowly, drown your tree's roots quickly, and kill the tree pretty quickly. Just like this:
So any time you plan to dig below grade in clay, heed David's advice and first assure drainage
from the deepest part of that hole to some LOWER part of your yard!
So if you are going to amend deeply for trees, first assure the holes will drain down to some lower point that you don't mind accepting the runoff.
My experience is with amending finite, relatively shallow raised beds, (and planting shrubs for neighbors decades ago). So anything I say about trees should be viewed with skepticism.
But I have read advice about trees, that suggest tree roots spread SO far and deep that amending is a real challenge. The tree roots tend to fill any reasonably-sized amended hole rapidly, but then may NOT ever leave their planting soil and penetrate the soil outside the holes. If they do that, and the clay is quite hard, the trees might as well have been planted in a sunken pot the size of the amended hole.
Since it is impractical to amend the entire area that the roots will ever need to penetrate, maybe "blend" the amended soil in the planting hole with the surrounding clay. If the transition from good to bad soil is gradual, the roots are more likely to make the transition from pampered soil to clay.
We had dogwoods when I lived in Connecticut, and again in New Jersey. That soil was all un-amended clay soil with rocks - not TERRIBLE, 100% clay, but very poor "clay soil". They did fine, or at least reached very old ages without problems.
I would only amend soil for trees if I was very ambitious AND knew that the trees in question really, really needed better soil.