Can flooring the loft restrict airflow and cause dampness?

Yes, if done the traditional way of fitting floor boards directly on to the joists, or onto timber batons placed on top of the joists, this prevents air from flowing across the roof space.

The warm, humid air rising from the house may condense on the cool underside of the decking and cause dampness and rot. A LoftZone deck will be raised 279mm above the top of your joists. This is to allow for a full depth of loft insulation (up to 350mm, measured from the floor of the loft) plus an air gap above the insulation and below the boards.

(LoftZone has taken advice from the Buildings Research Establishment for the size of the air gap during the design phase – hence the 279mm.)
LoftZone Airflow