Can I use bar tape on my (non race bike) bike with flat handles (not drop bars)
You can use any road tape on a flat bar. The main reason people do it is to make the grips thin and firm. Even a thick tape will be thinner than a thin grip. It's important to choose a wrap orientation where the torque from your hand is working the tape in the tightening direction. For a typical flat bar that means turn the tape clockwise looking at the bike from the right or counterclockwise from the left. Usually it works better to locate the finishing tape on the end of the bar as opposed to the brake lever because you want to avoid twisting on it directly, but that part depends on where you prefer to put your hands on the bar.

Finding the wrap orientation that resists loosening for you depends on habits and weight distribution and can tend to require some experimentation, but most riders find there to be one that works best.