What were the experiments and works that suggested kinetic theory of gases and proved that the static theories were incorrect? What are the experiments which could not be explained by static theory?
How can one conclude that these theories are insufficient to explain the experimental results?
 A: I have searched , and it is a sobering search. All reviews start and stay on the way the theory developed. It does not seem that there was a decisive need to go further than the thermodynamic theory, but the history shows that they did, and it was all theoretical! An example is in this link, ( also of course in wikipedia).
As far as I can see, the thermodynamic properties of fluids and gases were known and measured at the time, and the  kinetic theory developed in order to fit the already there observations on temperature and pressure etc, with a new model that opened new possibilities.
One can find now a number of experiments that demonstrate molecular behavior etc, but the theory developed without more experimental observations than the thermodynamic ones.
One could say that the experiments for Avogadro's law were the ones really depending on the kinetic theory and validated it.:

Experimental studies carried out by Charles Frédéric Gerhardt and Auguste Laurent on organic chemistry demonstrated that Avogadro's law explained why the same quantities of molecules in a gas have the same volume. Nevertheless, related experiments with some inorganic substances showed seeming exceptions to the law. This apparent contradiction was finally resolved by Stanislao Cannizzaro, as announced at Karlsruhe Congress in 1860, four years after Avogadro's death. He explained that these exceptions were due to molecular dissociations at certain temperatures, and that Avogadro's law determined not only molecular masses, but atomic masses as well.

These organic chemistry experiments may be the first validating the kinetic theory.
