"Trickle-down" was a term coined up by a comedian. It's nothing more than a pejorative term used by the left.
Allow me to rephrase: There aren't any economists who believe in the "trickle-down" theory that leftists like to assume people do.
The basic premise is that a rich guy paying a few guys to wash his Corvette would make those particular individuals better off simply because the wealth "trickles down." The most obvious rejection to that idea comes from the fundamental economic acknowledgement that the poor have a higher marginal propensity to consume (thereby a less marginal propensity to save), and thus capital spreads quicker and further.
"Rich spending for whatever reason somehow helping the poor" is a strawman, much like how climate change deniers tried to seriously argue that more snowstorms means the planet isn't warming.
The whole argument stems from a premise that even the most ardent leftists of economists believe: Investment leads to growth in total output. Of which there is a mountain of evidence and empirical studies backing, much more so than any done for arguing the negative effects of inequality.
Decades of economic studies have lead many to the conclusion that investment incentives are thereby good for growth and thus, that taxes on savings/investment should remain low. The more affluent an individual is, the more likely he is to invest, and thus in policy, this ends up turning into a tax break policy in which the rich benefit in a greater immediate direct margin than the poor do.
Regarding Kansas, context is key. Comparing the economic performances of two separate states (over such a short period of time, nonetheless) is hardly any different than comparing the economies of two different countries. Resources, inflation, production history, these are all extremely relevant.
You're far better off getting a look how well Kansas is doing by looking at figures for how it used to do in the past, and the numbers paint a much brighter picture.
The early results are quite consistent with those reflecting the tax policies of other states: States with little to no income tax experience far, far greater growth.