Which factors affects the reaction between magnesium oxide and zinc?

Magnesium is higher on the activity series than zinc, meaning that if these two chemicals are placed together the zinc will not replace the magnesium. Basically, these two are really products of a replacement reaction between zinc oxide and magnesium, and as such should not react again.
The full reaction would be 
zinc oxide + magnesium -> magnesium oxide + zinc
and is non reversible.
Replacement reactions like this are pretty easy to solve with an activity series table. If you have a reaction in the form A + B-C -> A-C +B, even by looking at one side you can figure out where the reaction goes. If you see A + B-C -> ___, where A and B are metals or halogens, you can use an activity series to see if a reaction will occur. If A is of a higher activity than B, then the C will displace to combine with the A, leaving A + B-C -> A-C + B.