There are two strategies to change flags: when OneHomotopy is set to true (default) it uses straight line homotopies to change flags, but assumes the initial flags are generic.
When OneHomotopy is set to false, it makes gradual changes in the flags by changing one column at a time, and using only linear homotopies, but in this setting, it generates polynomial equations using all minors of the incidence conditions (thus is not very effective).
The object OneHomotopy is a symbol.