Can I charge my car battery with my jump kit?

What is in this jump kit? Just jumper cables? Or is it the kind that has a small transformer with one end that fits into your cigatette lighter and the other plugs into a wall socket 120VAC?

You have to get power from somewhere. Jumper cables won’t help you unless you have a kind neighbor. The transformer will work – but slowly.

It’s like one of these. It’s a Husky 400 amp rechargable jump kit. Basically it’s a giant battery connected to a pair of jumper cables that will let you jump start a car without needing another car.

My big concern is that it’s mainly set for larger output (obviously since it needs to be strong enough to start the car) than a normal car battery charger. I don’t want to use it to charge my battery if I have a good chance of wrecking my new battery.

That won’t work. And that 400 amp output is only for a few seconds. For constant output… well, forget it.

What you can do is start your car with that “whack pack” and just drive around for about half an hour. Idling won’t work; you need to keep the RPMs up n order to charge the battery. I’ve done that before. Hell, I did it last week when I forgot to shut my headlights off when I rolled into work. I got a jump from a co-worker, drove 25 miles home, and the battery has been fine since.

I would not leave that on the battery for more than a few minutes. That unit is for starting the car, but you knew that already.
Here’s something you can try if you are desperate, have a voltmeter, and are willing to keep an eye on the battery.
You need at least 10–11 volts to crank the engine.
A typical battery alternator will put out 13.6 -14.4 volts when charging the battery. Clip the unit onto your battery and check the voltage at the leads. Now plug the unit in and check the voltage again. Is it still in the same range? The boost box are built to attach to dead batteries and then have a big surge run through them when you crank. It is possible the unit has an internal regulator that cuts out and protects the unit from damage.

I would not do the above for long.

Or you could just roll the damn thing down a hill. I did that to my wife’s car once and whoever says you can’t start an automatic that way is full of shit. It does take more speed though.