How long is the duration of a flash of lightning?

Arago has demonstrated that it does not exceed the millionth part of a second.

With what velocity is lightning, or the electric fluid which gives rise to its appearance, supposed to move?

Not less than two hundred and fifty thousand miles per second.

By whom was the identity of lightning and electricity first established?

By Dr. Franklin, at Philadelphia, in 1752.

The manner in which this fact was demonstrated, was as follows:

Having made a kite of a large silk handkerchief stretched upon a frame, and placed upon it a pointed iron wire connected with the string, he raised it upon the approach of a thunder storm. A key was attached to the lower end of the hempen string holding the kite, and to this one end of a silk ribbon was tied, the other end being fastened to a post. The kite was now insulated, and the experimenter for a considerable time awaited the result with great solicitude. Finally, indications of electricity began to appear on the string; and on Franklin presenting his knuckles to the key, he raised an electric spark. The rain beginning to descend, wet the string, increased its conducting power, and vivid sparks in great abundance flashed from the key.

Why was the kite insulated when Franklin fastened the key to the post with a silk ribbon?

Because the silk was a non-conductor, and would not allow the electricity received upon the kite to pass off by means of the string to the ground.