How do I determine expected harmonic frequencies and corresponding amplitudes in a case of synchronous machine?
If you are asking about wound-field synchronous machines, you probably need to look at older literature and text books. Recent research is more concerned with permanent magnet machines. Wound-field synchronous motors are generally only constructed in high power ratings above 2000 Hp (1.5 Mw) or so. Only about a half dozen manufacturers construct them. Smaller synchronous generators are constructed for engine-generator sets, but they are generally manufactured by or for engine-generator set manufacturers. It may be difficult to find design details for any wound-field machines.

For permanent-magnet machines, you should be able to find study results and data in more recent literature and even advanced design texts. You may need access to a pretty good engineering library.

It might be helpful to search for standards that might specify allowable harmonic amplitudes.

I have an old text that has data for a 2500 kVA, 32 pole generator. It seems to show about 2% for the 3rd, 9% for the 5th and 3% for the 7th.