The device used on Three Kings was basically just a large syringe with a pressure release valve on it. This is to allow built up air to escape the thoracic (chest) cavity. If not released the pressure builds up until the wounded person cannot breath...I think the term is called tension pnuemothorax.
There is no one way to treat a sucking chest wound. I keep just your basic plastic wrap for the purpose. Put a piece over the center of the wound and tape it down on 3 corners. When the person inhales it will be pulled down creating a seal and keeping air from entering the chest through the wound. When he/she exhales the seal will be released allowing any air to escape. You can also use a gloved hand for this purpose if necessary. Place your palm tightly over the wound upon inhalation and remove it for exhaling. There are all sorts of variations to the theme, but achieve the same desired results.
For my kit, I use a small ALICE pack. I have lots of gear and this bag hauls it all fine. The items I keep are plenty of 4x7" battle dressings, gauze, bandages, eye dressings, cravats, tape, scissors, small light, blood pressure kit, airways, cpr mask, thick exam gloves, saline, peroxide, alcohol, bee sting and snake bite kit, material for soft splints, trauma dressings (large type), candy for diabetics, stethescope, band-aids, burn creme, cold packs, aspirin, Tylenol, and some Benadryl for allergies and such. I have lots of other stuff, but those things are what I usually have to reach for.
I am not certified in using IV's but I know how should I ever find myself in a situation where it was do or die. I would not recommend this in any other situation though other than an absolute last resort. Non qualified people could get in lots of trouble for doing this if something went wrong. Leave the IV's and other invasions of the body to paramedics and nurses.
For anyone interested in first aid I would highly recommend that you take a First Responder or EMT course. This is what most fire departments and rescue squads train their members in. Paramedic is more advanced but costs more to take and lasts about 2 years. But any first aid course is terrific. The skills you learn may someday save a life...maybe even a family member. Now track down a class and enroll in it! Now!