The premise for the model is, the "chain reaction" effect, caused by the radioactive elements that are floating in the atmosphere.

There would be no chain reaction in the atmosphere. That requires both particularly high-energy free neutrons (from the decay process) and what's called critical mass (which, when you think about it, is actually "critical density") in order to be self-sustaining, which is why they're called "chain" reactions.

Elementary nuclear physics, my dear Watson...

Thus: [a] You don't get the critical concentration from particles dispersed in the atmosphere; The single naturally-occuring element capable of spontaneous chain-reaction is uranium, which is also the densest natural element -- not the sort of atoms to remain airborne for long (and how did they get there?).

There is geological evidence of a spontaneous chain reaction occurring in a natural uranium concentration underground, at a place called Oklo, in Gabon (West Africa). There's more information here that you might find useful.

The assumption: Fission products that are "expelled" by the radioactive elements that are floating in the atmosphere can increase the kinetic energy of the air molecules.

Notwithstanding that radioactive [b]decay is a different phonomenon than fission... let's postulate that you're right. You need to look at available data on concentrations of natural unstable isotopes (the best known is carbon-14) that are demonstrably present in the atmosphere, and how they decay, including what kinetic energy is available. Take an average collision, multiply it by the parts per trillion (or less?) available in the atmosphere, transform the resultant KE to a rise in temperature (the math is out there somewhere) . . .

Then compare -- orders of magnitude will do -- to radiative heating from the sun.

Look at it this way: the people who are concerned about global warming (myself included) don't count man-made sources of heat among the causes -- or volcanos, for that matter. They're negligible. How much more negligible will be the contribution you've deduced might be possible?