How do I calculate magnetic flux?
That link you provided, 'tables' gives nice curves of B and H for their various materials, along with 'load lines' for the demagnetising force.

You can use an equivalent of 'ohms law' to find the field. Think of the magnet as a battery, a source of H. The terminal current will be B, as B rises, the H will fall as a result of its internal 'impedance' (reluctance). It is H that forces a field through materials between the magnet faces.

To a first approximation, all of the H will be 'dropped' across your high reluctance air-gap. In comparison, the iron pole pieces have negligible reluctance. 

The curves already have a load line drawn on them. The flux and H field will be at the intersection of the load line, and the magnet loop. I suspect the load line labels are normalised to the magnet length, check with that supplier, I'm not going to devote the time to investigation. You have to make sure you understand what normalisation has been used with any set of graphs. If that's the case, and for the example of N35 material (just the first one on the list), you see the 1.0 line, which means an airgap of length equal to the magnet length, it intersects the curve at 1.1T (20C line). If you halve the airgap (2.0 line), you get only 1.15T, if you double the airgap (0.5 line), you drop to 0.6T.

Obviously the reluctance of the iron pole pieces will lower the field very slightly, and the reluctance of any inadvertent airgaps between magnet and pole pieces will lower the field a lot.

Also obviously, there is such a range of motors available, that getting one of the next size up from your 'unique' specifications will be far cheaper, faster and more efficient than rolling your own. However, as a learning and machining exercise, go for it!