Fco is a parameter is the empirical column buckling curve used for "short" columns. For long columns, Euler's formula applies. For short columns, plasticity is a factor, and empirical formulas are often used. I think the more "modern" aerospace approach would use Euler's equation with the Tangent Modulus, where long or short is automatically included.
The transitional L'/rho value referred to is the transition between long & short columns. If your L'/rho is greater, you have a long column, which is evidently the case the author had, and you can use Euler's formula. Since he had a "long" column the author does not go on to show the short column formula, which would be a linear function of L'/rho containing Fco. The Johnson-Euler formula is another empirical short column formula. It is parabolic and is often used for steels, whereas a linear short column formula is often used for aluminum alloys.
I do not have a copy of MIL-HDBK-5C to confirm this. Newer versions of MIL-HDBK-5 do not seem to have these formulas. Similar (or identical?) equations appear in Bruhn, chapter C4.5 titled "Column formulas for aluminum alloy tubes". He gives different forms of the equations depending on the exact alloy.