I cannot figure out how to level up to lv 31 on a hero. Trying with either Malcolm or Doc Gray. ..

Evolving requires Combat manual items. There are different levels of these that you need to get from completing campaign levels. You will need to work through the campaign and also repeat levels many times to farm for these items. At each evolve point of the heroes you need more and more of the combat manuals.

When you press the Evolve button to see the 'Evolution preview' of any hero you will see the icons for the combat manuals that you need above the Evolve button and thhe numbers that you currently have.