First aid kit basics
First, I think it should be said that if you carry a firearm and are prepared to put holes in people who threaten you or someone you love, you should be equally prepared to plug holes in case things don't go according to plan. A medical aid kit can range anywhere from a small pouch that you can carry with you at almost all times, to a backpack capable of treating a mass casualty situation. The medical kits I will cover are generally more concerned with fixing trauma related injuries on the spot, with the intention of getting the casualty stable while real medical help gets to the casualty. If you are considering acquiring a set-up like this keep in mind, these supplies and equipment will not magically fix the situation, you must be trained and proficient in their proper use. As a reminder, I am not a medic, these are all tool that I carry to extend my probability of surviving a deadly encounter, I am but a ground pounding grunt. Also, this is not meant as an advertisement, but I will be showing what I run with and where to find it.
This is my medium sized medical kit, it clips onto my regular belt, my battle belt or any other piece of my MOLLE covered kit. The black rip-chord being held down by my lovely assistant, when pulled allows the pouch to drop free of the mounting for easy one-handed use. I usually run with this as a nearby kit, it's just a little too big to not be bulky when I wear plain clothes. I do have a smaller kit that I generally carry on my person, which does alright but I like to have this one nearby as it covers a better spectrum of trauma care. Basically, my small kit is there to help me limp to this kit, where I can hopefully stabilize and wait for real medical help or push through to real medical help.
Once the blowout kit is opened there is a few items that are only secured by bands that I could easily rip out under stress as well as some other items that are secured by the elastic strap. The two tourniquets are easily removed to allow for a quick application, odds are good if I need to apply a tourniquet I will not be in the mood to fight some elastic straps. I was running the old Combat Application Tourniquet (CAT available here), which were widely available from my time in the army and I was used to working with them. I recently upgraded to the SOF-T Tourniquet (available here), mostly because I needed to plus up on some and these came highly recommended from some high-speed medics. I also carry a uniform repair patch for a quick, waterproof patch that can be used to set gauze or plug a hole fast.
In the elastic straps I have a pack of quick-clot combat gauze (available here), a cravat with two freakishly large safety pins (available here), and a Olaes Modular Bandage (available here). With these I can cover a large swath of wounds and stop most of them from bleeding.
The exact contents of the kit don't need to come from the links provided but I would suggest at a minimum: Tourniquets (preferably 2 for leg wounds), gauze, cravat bandage with pins, and an Israeli or Olaes bandage. Obviously, the kit only works if it's nearby when it's needed and whoever is using it knows how. I highly recommend getting a kit and getting trained up on the items and how to provide care.