"already existing" is redundant -- I would just change it to "over your WiFi network" or even just "over WiFi"

I don't know if we need to add a comment about distro support, but I would change the addition to something like "Any disto which supports Qt 5"
Better to be specific about what "little work" is needed :)

These typos were already here:
"This explains how to install KDE Connect on your computer. You will also need to install it in on your Andriod device and pair it to your computer in the app if you want it to be any useful."

But I would actually reword this to:
"These instructions explain how to install KDE Connect on your computer. You will also need to install it on your Andriod device and pair both devices before you can use this app"

(I prefer "pair both devices" vs. "pair it to your computer" because it avoids mirroring "your computer" in both sentences. It sounds more natural to me)

I would leave this sentence as it originally was. "might" means something like "Oh, well, we don't really know" but "should" means "We expect that it will work even though we don't officially support it" (And I think it does work?)

Don't you have to specify that we are channel #kdeconnect on freenode? I know almost nothing about IRC 😂

Maybe make testing this a GCI task?

Yes we do, good catch.