I know that what you're going for is to solve inequality by working within the means of the established political system, and that you're wondering if there could be something like a startup or company that somehow makes a profit by reducing inequality. After all, when starting a company the first problem anyone should solve is "What is the need" and economic inequality is a pretty big need.
Unfortunately, I just don't think every problem can be solved through that lens. Companies can earn money by creating something of value, or by making something cheaper. Facebook connecting the world together was creating new value, and Google making information easily/freely available was a drastic reduction in the cost of discovering information. Both of those services created value. The problem of economic inequality is not a problem of needing more value, it's a problem of poor distribution of value. That's a problem companies are not good at solving. Companies are usually terrible at solving those problems.
The other side I see you going for is that the government seems unreliable, so you'd rather there was a solution -- ideally one that's scalable -- that didn't rely on forces outside of your control. My best guess would be volunteer work and activism, which doesn't have to go through the government. Supporting local businesses and encouraging your neighbors to do so helps your local economy. Food banks and homeless shelters are great, and so are public libraries. Big brother/sister programs, little league sports coaching, volunteering at after school programs -- all good ways to help.