I usually do pretty much as ataradov suggested.
If you end up with a few solder bridges after you've drag-soldered all the pins, don't sweat it, they can be removed by adding some flux to the affected pins, then clean the tip of your iron to get as much of the solder off the tip as possible, and gently swipe the tip along the bridged pins, from the IC outward toward the pad, some of the solder will migrate onto the soldering iron tip, removing solder from the bridge. If the first try doesn't do it, clean your tip again and repeat as necessary until the bridge is gone.
Also be careful when drag soldering not to apply any pressure, as this could bend the pins out of alignment or damage pads. Let the flux and solder do all the work of transferring heat from the tip to the pins/pads.
Lastly, there's no such thing as too much flux IMHO. Sure, you'll have a bigger mess to clean up once you're done, but flux is the magical ingredient that makes the solder flow nicely to where it's supposed to go. Drag soldering only really works with a liberal application of flux.