For best results and a chance of removing them in future then No14 (6.3mm) hex head stainless self drilling screws and No14 zinc plated (or anodised) U clip captive nuts. For the fronts the lower fixings also require plastic captive nuts but these generally come with the mud flap. If not then CZA4705L is the part number. Upper fixings need a 1” or 1.5” long screw and lower fixings may need a longer 2” or so screw. The captive U clip captive nuts are fixed around the holes previously occupied by the plastic fixings for the wheel arch liner which will need to be removed.
If you want to look OEM then the screws need to be black cross head self tappers but beware that because of where they are and the environment they experience they are traditionally nigh on impossible to remove after a few years!
Do not over tighten the fixing screws as this will cause the rear edges of the mud flaps to come away from their snug fit on the bodywork with an unsightly gap appearing.
2001 Vogue
Yes . . . . . . I do own the road