It won't. I'm sorry, but it just won't. There are several reasons why a kickstarter for academic/scientific research is doomed:
1) People underestimate the amount of money required to fund research. Starting this Fall, I'll be receiving a grant from the NSF for one year of funding. That funding pays me approx. $1800/mo, plus covers my health insurance ($800/mo), tuition ($5k/semester), and travel ($7000/yr). The university also provides me with facilities and access to faculty and thus have overhead that need to be covered. This grant is shared among 3 PhD students and totals over $180,000.
2) Progress does not happen in leaps and bounds, it happens in inches. Kickstarter projects go from conception or prototype to finished product. Research does not work that way. You go from previous algorithm to slightly updated algorithm. It's a marathon, not a sprint to production.
3) You get nothing. Kickstarter projects give you a cool gadget or game or piece of art or whatever. When you fund a Kickstarter project, you get to see a video of some prototype or sketches that look like they'll be awesome. By the end of it, it's finished and you have this cool new thing that you can enjoy. You will not get any cool new thing from researchers, because they don't even know what it is they're trying to make yet. At best they will produce a conference or journal paper, maybe with a neat little demo of low production quality, and then they're on to the next problem. Scientists are not interested in building production-ready toys, they are searching purely for knowledge. So you as the funder get nothing tangible.
4) Most science is boring to the average person. Researchers live on the edge of human knowledge. They are tackling problems for which there is no known answer. Odds are, if you're in a sexy area like neuroscience, robotics, etc., then the problems you want to solve have been looked at for decades by people much smarter than you. Thus, you are not going to make some gigantic breakthrough that leads to strong AI-- you're hopefully going to develop a new learning algorithm that performs 3% better than the state of the art on a handful of benchmark datasets. Exciting, right?
Overall, it'd be great if we had democratized funding that worked. Unfortunately, due to the costly, slow, intangible, esoteric nature of scientific research, it's unlikely that will happen. Most academics have a hard enough time convincing experts, who have dedicated their lives to the area, that their work is worth funding. I just don't see how it could possibly work.