I'm not sure what you are trying to do. You have a residue containing gold and mica? Or, to the contrary, is this in a matrix rock such as quarzite? If it's a residue then simply dump the gold and mica into a tall clear glass of water and the gold will sink much quicker....the difference so obvious that you just have to tilt the glass after the gold sinks to separate them.
I have to question if you actually have flakes of gold and mica....they will be quite distinct if you look with a hand lens. There couldn't be an element and a mineral easier to separate just by vibrating them on a sheet of paper. No fancy solutions or equipment are necessary. Even blowing on the residue will separate them.