TL;DR: No, Incoggo will not slow down your computer. Depending which apps you run, Incoggo may actually speed up web browsing dramatically.
Incoggo is a ‘local proxy’, meaning that all filtering occurs directly on your device. While Incoggo does add a few milliseconds of overhead latency (possibly less, depending on your CPU) to web traffic, Incoggo has been heavily optimized for performance, CPU, and memory usage, meaning the delay won’t be noticeable even for the most performance-attuned applications (think: FPS games, etc.); Incoggo typically uses less than 1% of CPU and less than 60MB of RAM. Additionally, the performance gains from running several apps – such as Block Ads or Block Trackers – will typically dramatically outweigh the additional overhead.