Giant Rome 2, had several flats in the front, now when I spin the front wheel while it's on the rack the front has a little bit of drag and stops pretty quickly after I let it go. It feels like disc brake drag.

Should I try and recenter the front caliper? Do I understand it that I should loosen the caliper fasteners and then pull the brake tight and then tighten them while holding the pressure?

Or should I try and center the tire with the skewer? Does a front skewer slide or can you adjust the centering by loosening the tight side and tightening the side opposite the drag?

The skewer doesn't position the wheel. It merely provides a pinching force to capture the dropouts against the ends of the axle. You would have to shift the axle in the hub to shift the position of the disc with respect to the forks, and this is likely not possible or proper. Assuming the disk is straight and running true, position the caliper for clearance per the manufacturers installation instructions. If you don't have them, they can almost certainly be found on the manufacturer's website.

Front wheel may not be is properly.

If hydraulic disc brakes you may have touched the lever and the auto-pad wear mechanisim kicked in.

First confirm that the ft wheel is properly secured in the fork, sitting straight and tightly held. Only then move onto the brake. The initial attempt to center the caliper/pads is as you described. But i would spread the pads with a cone wrench (cleaned off) first to re establish the pad movement amount. After there will be additional tweaking of the caliper position WRT the rotor. I find that if I slightly loosen the two location bolts then loosen one fully I can "walk" the caliper over a small amount. Slightly tighten the looser bolt, loosen the other and repeat. This one bolt at a time method seems to allow smaller amounts of pad centering w/o misaligning everything. This is very much like adjusting chain tension on a single speed. By working one side of the axle at a time very fine amounts of change can be had w/o much frustration. Of course this assumes a rotor straight enough to not be the rubbing problem. Andy.

Well I was heading out for a ride and it bugged the hell out of me that it dragged, eve though it was so slight.

I loosened the bolts that held the caliper to the mount bracket, squeezed the brakes and tightened it back up. Viola! No drag at all.