I've gone through the new book and worked to identify which formations and equipment would have been available during each war. Bear in mind, however, that the new game is not only meant to be played with what ever mix of equipment you choose, but it is also points compatible with the new 'Nam game, so you can mix and match (Israeli vs. NVA anyone?). Therefore any segregation of forces based on Six Day War or Yom Kippur War is purely optional!
As you can see from the chart above, given their position in the Soviet orbit during the time period, Egypt and Syria shared a great deal of equipment. There are, however, a few units unique to each nation based on what they were able to obtain in the early post-colonial era.
Hopefully this chart will be helpful as you build your forces from Fate of a Nation. I'll be adding Jordanian forces in the future as well as some modeling and painting guides. Watch this space!
Edit June 25, 2018 - Removed BTR-60 as a 1967 option - Syria does not appear to have purchased the AFV until 1970 based on better references than were originally available.