"trickle down" isn't a real thing, it's just a pejorative used against supply side economics, which is a mainstream economic view.
The basic account of "trickle-down economics", goes something like this. When you give a tax cut to a rich guy, he uses the money to buy party supplies for a celebratory yacht party. The guy who owns the yacht party supply store sees an influx of cash from rich guys spending their trickle down tax cuts on yacht party supplies and orders a pizza to celebrate, and gives the pizza guy a big fat trickle-down tip. As you can see, the tax cut started out at the rich guy, but before long even the lowly pizza delivery guy is getting a piece of that sweet trickle-down cheddar.
Notice an interesting thing about this account: it is fundamentally a _demand-side_ story. In this story, the trickling down happens as a result of people spending extra money on goods and services. It is not about creating supply. So it's _not even an accurate representation_ of supply-side economics. People rightly point out that it's a flawed story, because poorer people probably have a higher marginal propensity to consume than rich people, so you'd be better off giving the tax cut or equivalent transfer payments to poor people if you want to stimulate economic activity. Well, yeah, no shit, that's because this is a complete straw-man and no economist actually believes that this story is true.
What some economists actually do believe is that the path to prosperity is via the supply curve and not the demand curve. Making things cheaper to make and cheaper to buy makes people better off faster than just giving them money to buy things at existing levels of production. And the way to do that is investment—investment meaning, in the economics sense, spending on things like factories and equipment. There is a huge body of theory and evidence to support this idea—higher levels of investment do lead to faster growth. So supply siders believe that things like taxes on capital gains are harmful to the economy on the margin because they reduce spending on investment, and may even encourage spending on consumption, which is a bad outcome to the supply-sider. They also believe in reducing barriers on production—things like government regulation and income taxes. They also believe in, you guessed it, helping make sure that corporations don't go out of business amidst a once-in-a-century black swan event — call it a "corporate bailout".