No, it won't actually do harm to your eyes or vision. You won't be blinded by this. When the flash bang grenade burns, the flash light temporarily activates your light sensitive cells, causing blindness in a few seconds. After that, your eyes will restore themselves. They are just the light from burning magnesium. No virtual damage will be done to your eyes.
To make you feel better, you can turn your head away after your throw them out.
Actually your eye vision may be affected to some degree. But you will not get blind if you keep doing this every day. You should protect the eyes carefully. You could wear the protected goggles when you take this action. Or you should eat more food with vitamin C to moisture the eyes. In addition, the warm compress is also a good method.
You know, flash bang is the kind of weapon which is used to bother enemy's eyesight and prevent them fighting back for a moment. When people see the light from a flash bang, their eyes will be blind for a few seconds. You'd better close your eyes after you throw them away to avoid the huge damage to your eyes. Usually, if people just get harm from flash bang once, they can recover automatically. However, if you keep doing this every day, your eyes sure will get harmful damage such as the detached retina.