It's a good question, but not a good idea by a long shot!
Burning plastic at home is probably one of the nastiest things you can do to both the general environment and your own, personal, local environment, including the one inside your lungs.
Wikipedia's Incineration and Waste-to-energy plant make it clear that you need several disparate and simultaneous technologies to both
- achieve extremely high temperature and thorough combustion
- remove the remaining toxic and polluting gases and the carcinogenic compound-laced micron-sized particulates that go into lungs and never come out (except perhaps by making their way into your bloodstream first!)
The proposal is just a little like thinking that if we burn hydrocarbons in power plants to make electricity to run cars, why don't we just make our own fires at home and run little generators to charge our electric car batteries, or maybe even get rid of the middleman and each burn our own hydrocarbons right in our own cars.
Scaling is good!
The sort-of main reason that it's cheaper and less polluting to use electric vehicles charged by hydrocarbons burnt in central locations is the technological and economic advantages of scale. It is much, much cheaper to achieve high efficiency and relatively lower levels of environmental impact when (the newer) big hydrocarbon power plants can take advantage of the latest technology.
Making a "home" fluidized bed incinerator and producing sufficiently high temperatures to ensure thorough combustion and making a scrubber for gases and particulates at home would be incredibly labor and money intensive.
"Fire projects" at home are bad, dangerous and frequently illegal
Most communities have all kinds of regulations related to burning garbage at home. You might have intellectual arguments why what you are doing is good and safe, but when someone calls the sheriff or the fire department, good luck with that.