Chukovsky’s poem is animated a few times. Best know is the 1960 Boris Dezhkin version, which isn't aloud on youtube. You can find it here: www.dailymotion.com/eus347
This Boris Stepantsev version from 1979 is the one that is most loyal to the Chukovsky’s poem. Dezhkin quotes only the fist few lines of the poem, the rest is told wordless. Stepantjev quotes (almost) the complete poem. the story is this
Fly-Tsokotukha finds a coin and buys a samovar to celebrated her birthday. At the birthdayparty the spider kidnaps the fly. Then the mosquito comes to the resque.
directed by Boris Stepantsev
written by Boris Stepantsev
art directors Anatoly Savchenko, Ada Nikolskaya