I assume that the 'leg' is tubular steel with pre-drilled holes.
The problem with using countersunk screws is twofold, firstly that countersunk they will only make contact with the very edge of the hole and are likely to deform it over time and effectively become less tight. In this sort of situation you want the fixings to be providing a clamping force rather than being loaded in shear.
The other issue is that the screw heads won't sit flush with the surface which doesn't look very neat and can leave a sharp edge protruding which can snag on things.
Using plain washers may help with the first issue, at least to a degree but not the second. You can get cup washers which are have a recess to allow countersunk screws to sit on a flat surface but then again anywhere which sells cup washers is also likely to have flange or pan head screws whcih is what you really want.