Will the hinge on my Folding Primer Tray break?

No, the new Folding Primer Tray is produced out of clarified polypropylene, the first-choice for living hinge applications. Polypropylene is uniquely adept for living hinges because it does not break when repeatedly bent. The material also is resistant to fatigue, retains its shape after a lot of torsion, bending, and/or flexing.
You do not need to "condition" your Tray at all to prevent it from breaking.