A flash is useless for video; it will just flash and then be dark. You need a video light.
There are lots of video lights around that will fit on a camera's cold shoe (or hot shoe)... which, sadly, your camera doesn't have. You may be able to get a bracket which fits on the bottom of the camera, and provides a side handle with a cold shoe; look for "Triple Cold Shoe Mount Camera Extension Bracket" to see the kind of thing I mean. Make sure it fits your camera. But really, in any case, a camera-mounted light will usually look pretty poor.
A better answer is to either provide more light, like for example with more room lights, or a set of studio lights (again video lights, not flashes), or use a more sensitive camera. There is no communication between video lights and a camera for video; you just get the camera to expose for whatever light is available. So any video light would help.
Bottom line, I think you're just hitting the limitation of your camera -- a small-sensor camcorder generally will not do well in low light.
If you want to see what's possible with large-sensor cameras, I did some tests by candlelight: https://moonblink.info/MudLake/gear#Candlelight
