The main way you will get rid of flea beetle is to garden organically and grow lots of annual and perennial flowers amongst the vegetables which would attract in insects which prey on them.
If you don't want to use insecticides which kill every thing else, use a sticky board covered in something like petroleum jelly which you pass over the ground brushing the tiny plants. The flea beetles jump up and stick to this. Sticky yellow traps like the ones used for white fly in the greenhouse are also effective.
You can also grow 'trap' crops, which are things which attract flea beetle more than the one you are growing. These include some types of Chinese cabbage, radish, and so on.
Some people say growing catnip alongside the crop also works.