If I were to use a deep fryer, and then a flat griddle, at what temp and for how long should I par cook potatoes to later finish on a griddle as home fries?
I wouldn't deep fry potatoes to par cook them for use with anything other than future frying. That cooking method gives the potatoes a hard exterior that won't cook as easily on your griddle.
Instead for home fries I prefer to blanch my potatoes in boiling water. This makes them soft and absorbent to seasoning and the starch is pulled to the surface which then gets that nice crispy exterior that you want at the END of the homefry cooking process.
Oh and since your size will effect your cooking time I will just give you a ballpark 7-10 minutes but really you are looking for about 60-75% doneness.
Deep frying prior to griddle finish can yield fine results. Just like par cooking for future frying, you want them cooked just through, so the center will be soft and completely cooked on finish cooking.
5-7 minutes seems reasonable for discs or smallish (1") cubes. Cook until just less than fork-tender, meaning there is resistance at the center when pierced with a fork.
Completely cool the potatoes, then the finish cooking will give you nice, crisp surface and tender center.
As another poster said, boiling is a fine method also. The comment about 'open to seasoning' is not relevant here, as the seasoning will be on the surface and picked up by oil or onions, etc.. If you boil, same rules of just less than fork tender applies. Cool completely and drain to get good, crisp texture.
Per J. Kenji López-Alt, The Burger Lab: How to Make Perfect Thin and Crisp French Fries, "you should place potatoes and vinegar in a saucepan and add 2 quarts (1.9L) water and 2 tablespoons (24g) salt"
I've found this method to be yielding the best results.