I built a 300 sq. foot flex room in my basement over a year ago. Currently the only cold air return is between the floor joists above the suspended ceiling tile. I want to add a cold air return on the floor to draw the cold air off the floor in winter and pull the warm air down as the heat duct is in the ceiling. I can go into the main cold air duct, about four feet away from where it goes in to the furnace, with a four inch duct, then down the wall and use the space between the wall studs which is covered in gyproc as the cold air duct cutting a 4x10 hole in the other side of the wall for the return vent. Is there any issues with being this close to the furnace, back draft, etc?

There's no problem in the proximity to the furnace but using a stud space for a return is now illegal in most places. It has to be run in an actual duct.

The duct plan sounds fine but you have to realize that this new cold air return will greatly dimish the other returns service by this duct. Also bring down the warm air duct to the floor away from the cold air return. Warm air does "pull down" so easily as you might think, it rises on its own.