I have great success with floating row covers, also called spun bonded or remay. I keep them covered until they are big enough to shrug off the damage that the beetles do, which is much tougher on the plants when they are small. It comes in rolls in garden centers and some on line sources.

Start with floating row covers, but if the flea beetles are already on the plants other things will be necessary. Neem oil sprays or pyrethrin based sprays or dusts can help. Check the link for more information.

Here is a link that might be useful: Our Garden Pests

Floating row cover and a good thick mulch are the best preventatives. I cover my eggplant as soon as I put it out in the garden. The floating row cover also keeps the CPB damage to a minimum. I will also dust under the row cover periodically with DE if a few FBs are present.

I don't know why it works, but a light dusting of lime gets rid of flea beetles for me.

Because lime is extremely caustic and can burn the wee buggers (as well as you if mishandled) and is a dessicant as well.

I just tried this this morning and it is getting the flea beetles real quick. I got a couple of large bottles and filled them with water for wieght. I also brought out some of the tin pie plates that I have attached to stakes. I painted the bottles and one side of the pie plates "safety yellow" and then spread tanglefoot on them(a really sticky product I got at a local nursery- comes in a tub labeled for tree use). I already have some striped cuc beetles and flea bettles on them and I only put them out 2 hours ago. It seems to be working really, really well with the flea beetles that are all over my potato plants. I covered my eggplants with a row cover this year so they aren't having any problems. I am going to use the sticky traps once I have to uncover some of my other crops if I see some infestations again.

Flea beetles are annually my worst pest problem.

Yellow sticky traps are commerciallly available or you can make them like imtoobusy does. Either way--that's the most effective way to control flea beetles in my opinion, in additon to good garden sanitation.

It's too windy here in the spring to do row covers, so I can't comment on their effectiveness.

When the eggplant are young is when you're at the most risk, as they may not survive being skeletonized. When they get bigger, a leaf can take the occasional flea beetle bite a whole lot better than it can now.

I too absolutely SWEAR by my lightweight/insect-weight floating row covers & use them on EVERYTHING except caged tomatoes.

The only plants I uncover are those that require pollination once they begin to bloom, & even then I recover them at night. I've found that they not only deter insect pests, but deer & groundhogs as well.

However, if your plants are already infested, floating row covers won't help much at this point as you'll only be trapping the bugs beneath it. In this case I would use Safer Insecticidal Soap spray, which is usually available at most large home & garden centers &/or online.