What to do first in a basement? Dricore then frame on top? Or frame and then lay dricore?
The framing in a basement is non structural. The only weight on the walls is the wall itself and minor loads from shelving, etc.

The purpose of Dricore is to isolate everything from the floor and walls except the plastic spacing material on the bottom. Dricore is also installed with a small gap at the walls. If you build on top of the Dricore, the studs are kept away from any moisture that may seep through the basement floor or seep through the walls.

Keeping the studs from touching the basement walls also helps create a thermal break to assist with insulation. Additionally, an air-gap behind the insulation also increases the R value.

Build the walls on top of the Dricore. Pin the Dricore to the floor as directed.