What was the first plane that allowed walking during flight?
The first airplane with a cabin big enough for walking around was indeed a Sikorsky. This was the Sikorsky Russky Vityas, also sometimes named "Le Grand", a name which was given to an earlier, two-engined version. Oh, and the cabin included a washroom, too!



Sikorsky Russky Vityas (picture source)

It was the first four-engined airplane in the world and the biggest airplane of its time. It flew first on May 10 (or 13, depending on the source), 1913.

Quote from Wikipedia:


  After the Russky Vityaz's first test flights between 10 and 27 May
  1913 (Old Style dates), it was established that a passenger could even
  walk around the cabins without causing any problems to stability.




Early Le Grand version with two engines (source)