Is there any video evidence of animals raining from the sky?
Brian Dunning already went into this extensively in episode 4170 of Skeptoid: It's Raining Frogs and Fish 


  In 1901, a rainstorm in Minneapolis, MN produced frogs to a depth of several inches, so that travel was said to be impossible. Fish famously fell from the sky in Singapore in 1861, and again over a century later in Ipswich, Australia in 1989. Residents in southern Greece awoke one morning in 1981 to find that a shower of frogs had blanketed their village. Golfers in Bournemouth, England found herring all over their course after a light shower in 1948. In 1901, a huge rainstorm doused Tiller's Ferry, SC, and covered it with catfish as well as water, to the point that fish were found swimming between the rows of a cotton field. In 1953, Leicester, MA was hit with a downpour of frogs and toads of all sorts, even choking the rain gutters on the roofs of houses. The stories go on and on: More frogs in Missouri in 1873 and Sheffield, England in 1995, and more fish in Alabama in 1956.


From everything he read, waterspouts seem unlikely:


  Not once in a single case of several dozen that I read was there ever a report of a tornado or waterspout in the vicinity, or even at all, no matter how far away. I conclude that waterspouts have no connection, either hypothetical or evidentiary, to the phenomenon of frogs, fish, or any other animals, falling out of the sky.


For frogs it seem to be coincidences of bad weather and frog migration.Well, not really coincidence: they probably migrate more (often) when it's wet.
And for fish:


  You don't find mass migrations of fish crossing overland, do you? Well, maybe not mass migrations, but believe it or not, there are fish species that occasionally take to the ground in search of better waters. There are many species of "walking fish" in the world.


The main reason that they did not fall from the sky is simple:


  Drop a fish off a building, and that's a dead fish


That's why you won't find actual videos.

Brian concludes:


  Go back and read any story you've ever seen about frogs and fish falling from the sky, this time allowing for the possibility that the animals were already naturally on the ground when the witnesses first discovered them. Allow for the possibility that some elements of the report, like the falling part, could be based originally on witness conjecture or assumption. 


Which is more or less what Stephan also writes in his answer.