Ok here's the thing. I was lucky enough to get a part time job that gave me a Kodak DX7630 digital camera. There is no slave snyc in it. My idea was though to connect an off camera flash with a slave unit on it that would be trigered by the on-camera flash. Will this work, or will it just overpower the picture?

Where there is a will, there is a way. Mount the camera and external flash on a flash bracket. use a piece of aluminum foil and tape to deflect the on-camera flash straight up to the slave sensor on your external flash.

The camera's internal flash can fire a slave on a remote flash - it's pretty easy to do it that way. Do you have any manual settings on the camera? If not, I don't know how you'd get anywhere near a correct exposure, unless just by luck.

If you can adjust the aperture, then you could either go fully manual with the flash and measure it with a meter - or an "Auto" mode on the flash (non-ttl, of course) and set the aperture to the distance range you need. Something like a Vivitar 283 would be a good choice for either of these two examples, depending on how much power you need. Of course you'd have to add the slave to fire it, too.

I know someone who shot a catalog of small products with a Coolpix like this. He used the internal flash to fire studio strobes, and put a 2-stop neutral density filter on the camera lens so that the light from the internal flash wouldn't be seen.