A mod should probably move this over to equipment... BUT
3rdMan, a full picture and description of your setup would be the best place to start. There are some troubling things in what you've posted so far, but I don't want to jump to conclusions.
Where to start..
1)I'm assuming there is no substrate in your cage, if there is, remove it as it is unnecessary and a giant health risk to your cham on a number of levels. Bare Bottom is the way to go.
2)I'm also assuming that it is a screen cage.
Any kind of recirculating water feature is a bad idea. It breeds bacteria that can be very harmful to your cham. Most aquarium type filters actually depend on generating bacteria and will only make the situation worse.
Your plants should be in pots, the bottom of the pot should be filled with large gravel for drainage. Then add the plant and the soil. The top of the soil should be covered with more large gravel so that no soil is available to the chameleon.
The pots should be elevated slightly off the floor of the cage, either with some kind of feet, or I actually use cookie cooling racks. This will provide adequate drainage for your plants, and allow you to water as much as you want.
Your cage should be elevated on some kind of stand, the floor of the cage should have some kind of drain in the center of it, the weight of the plant over it will make the water flow towards it. You'll have to DIY the drainage system to get the water to go where you want it to go, mine goes into a 5 gallon bucket.
To automate the dripper, and the misting, you'll have to spend some money. You can use an automated misting system to both mist the enclosure, and fill a dripper with a little DIY skills. Essentially in addition to mounting your regular misting nozzles, you mount a 120degree high flow nozzle in the lid of your misting container, and whenever your misting system goes off, your dripper will also fill with water and continue to drip long after the misting session is over.
Something similar to this could also be achieved with an aqua-lifter aquarium pump on some kind of timer.
Obviously the chameleon will benefit from having clean water available at all times, but it isn't practical. Using one of the systems I've described you could offer water for around 20-30 minutes at a time, 3 times a day and be perfectly fine.