Maybe 5 minutes. Don't forget there is also a boat if you want to rest your feet or do something different. Just look at the internation gate. We had planned to do this but it was pouring rain ALL DAY!
In my opinion, no. It is quite close to the International Gateway, so it's not far from WS. If you were walking from the far side of FW, that would be quite a walk, though! There are some wonderful maps that show the route posted online by a DIS member, Robo. I hope it's okay for me to post the link to all the maps: http://www.stitchkingdom.com/maps/
From the International Gateway to the Flying Fish (right about in the middle of the Boardwalk Inn it's right at 600 yards according to Google Earth.
Not that far at all.
Comparative distances:
Front door of the Land pavilion to Test Track: 466 yards
Front gate of Epcot to the railing of World Showcase Lagoon: 602 yds
Distance the Germans must walk to invade the France pavilion: 639 yds
Distance from the American Experience to Canada, our northern neighbor: 797 yds
Distance from the American Experience to Mexico, our southern neighbor: 717 yds
Going from Mexico to China (normally a long trip across the globe): 210yds
5-10 minutes to the Boardwalk or the Beach Club from the International Gateway,10-15 minutes to the Dolphin or Swan and 20-30 minutes to DHS,all depending on your walking speed.