Cover your eggplant with row covers and keep them covered until they start to bloom. Then you have to uncover them for pollination, but at that point the leaves are MUCH less appealing to the flea beetle.

I companion plant beans with potatos. The potatos keep away the mexican bean beetle and the beans keep away the potato beetle. One of my more successful companion plantings. Flea beetles are tougher. Have you tried diatomaecous earth? Google it. It is a powder that is actually sharp microscopic exoskeletons of an ancient creature. Works well against many insects. try to use it only where you need it because it will also kill beneficials. I had something in my cowpeas a week ago and the Diatomaecious earth seems to have made them go away. the good news is that I bought mine at Lowes so you don't have to wait for an internet order. This year I am trying radishes for a companion plant to combat squash bugs, cucumber beetles and flea beetles. I read that if left to go to seed they will deter such critters. I'll let you know how it works. If anyone knows of a good companion to deter flea beetles I would love to hear about it.

Because there are a number of insects that could be and which they could be can also be limited by the location os the plant knowning where you are, aside from generally somewhere in Canada, would be helpful. Possibly taking a bagged and sealed sample to your nearest AgCanada office could be of some help too.

I have a similar problem and am using this recipe with some success: 1 bulb garlic crushed, 1 onion crushed, 1 Tbl cayenne powder, 1 Tbl liquid dish soap, 1 quart of water. You can spray or just splash/rub it on the leaves by hand. Many find that a mild dish soap solution alone will work. Good luck!