There's no quick answer but ...
Also I am not familiar with that instrument other than having seen them on eBay. I recall discussing them on either the flute or whistle forum. Ah, I see you were part of the most recent threads on that fife.
Here was an earlier thread.The place to start is to position the face of the cork at a distance from the center of the embouchure hole equal to the bore of the fife at the embouchure hole. So if the bore of the fife is 1/2" then you measure on a dowel 1/2" from the end and make a mark on the dowel at that point. Get the cork into the bore in the fashion described by Stu. Once the cork gets close to the embouchure hole you can use the tick on the stick to set a starting position for tuning.
The cork's position will tune the octaves to bring them into alignment. If you place the cork in the starting position and the second and third octaves are flat to the first octave then you nudge the cork towards the embouchure hole. If the high octaves are sharp of the low octave then you move the cork away from the embouchure hole. The face of the cork should not get to the edge of the embouchure hole. You can perform the octave alignment test on several notes as well.
All of this is strictly dependent on the assumption that you already play the fife and that your blowing technique is not going to be in question as you position the cork.
There are several sites in the Internet devoted to playing the fife. Each likely has a section on tuning. Google will help you find the right pages. They should tell a similar story to what I have tried to describe.
You could also post your inquiry to the flute forum to see if any of the other American Plating fife owners show up too.
Feadoggie