It follows immediately from Theorem 3.1 that,
Corollary 4.1: Any cone, which admits a flock, admits a linear flock.
Flocks which are not linear are called non-linear flocks. Given the ubiquity of linear flocks, we are more interested in the existence and construction of non-linear flocks.
There are cones which admit only linear flocks. For example,
Proposition 4.1: A flock of any cone in PG(3,2) which has a flock, is linear.
Proposition 4.2: If S is the complement of a line l in (i.e., an affine plane) then C(V,S) admits only linear flocks.
There are other, less trivial examples.
After we introduce coordinates and certain normalizations, the linear flocks will be easily identified algebraically.