Sometime after Kitchel entered the Cave of the Three Treasures with Ringleys, she acquired a large backpack that she has been using to carry her stuff. All her stuff. Including stuff that shouldn't rightly fit in there.
Stop-- Hammer Time.
In the Dragon Knights universe, there are multiple dimensions and worlds. It is possible to open up the space between them without creating a portal to anywhere in particular, kinda like making your own little pocket dimension for personal use. You have to be pretty damn powerful to do it, though, and I think Cesia is the only one who really utilizes it, since she has wtf power already. Members of the Dragon Clan can access their weapons through a little dimension like this located in the palm of their hand, and Thatz has proven that it's possible to stash other belongings in there as well.
Kitchel's bag functions as one of these pocket dimensions; it's basically her compensation for not having the magic required to make them herself.
It's never explained where she got the bag itself, but I assume she asked the Dragon Eye (more on this in a bit) for it, the same way she got a bunch of the rest of her stuff. Even though there's a lot of stuff in there, Kitchel never seems to have a problem finding what she wants. This is also presumably due to its magical nature.
List of Stuff in the Bag (and explanations)
*The Diolasis (The Diolasis is one of the Three Treasures that Kitchel obtained for the Dragon Lord. It is basically an extra-special Dragon Eye, although she cannot use it nor can anyone else in LSG unless Cesia or Raseleane show up. It looks like a crystal ball. Kitchel doesn't know what it is, although she suspects it is related to the Dragon Eye.)
*The Raiketa (The Raiketa is the second of the Three Treasures and is, basically, a magic gun. As before, there are restrictions on who can use it and the only one currently in LSG who could work it is Rath [although in its current state it still needs more power, so.] Kitchel doesn't know much about this one, either.)
*The Salbacion (The Salbacion is the third of the Three Treasures. It is basically three small glass vials of holy water [although she has already used one], at least one of which is needed to "activate" Raiketa.)
*The Map (The Map is special. It's actually made up of a bunch of little stone pieces kept in a pouch, but it forms itself upon request [and appears to be able to take on a more typical form if desired] with use of the Dragon Eye. Technically you could put it together by hand, but that would take a realllly long time, as the pieces are all blank. The map remains blank until united with the little green stone [more on this in a bit] on Kitchel's necklace, whereupon it shows the way to the Three Treasures. If you already have the Treasures, it'll just show you wherever you are at the time. It's pretty useful. :3)
*The Dragon Eye (The Dragon Eye that Kitchel has with her is one of two in her world and is a magical wish-granting item taken from Lady Raseleane's eyes wtf much like the Diolasis. This one can be used by anyone, however, and it is possible to break it, although only with an amazingly vast amount of power. It has been used
here, in one of the chibi-threads, to give an idea of the sort of things it can do.)
*The Blizzard Blade (A long and thin sword made out of ice whose name doesn't translate well into English. There was a curse laid on it that would freeze whoever touched it, but Kitchel [following instructions given to her by a specter] broke the curse by using one of the vials of the Salbacion on it. It is an immensely powerful weapon although picky about its wielder. She is supposed to give it to Thatz when she finds him.)
*Holy Water (Like the Dragon Eye is to the Diolasis, the Holy Water is to the Salbacion. Kitchel has several vials of holy water in her bag and it has been said that they work well against the undead.)
*Heaven's Aqua Balls (Basically, balls about the size of large marbles, filled with vast amounts of water. It's like you compressed a swimming pool into a walnut.)
*A Pick and Shovel (Yeah, okay, so Kitchel used the Dragon Eye to get these before she got the bag. Knowing her, though, I'm willing to bet that she held on to them.)
*A Fishing Pole (...She might have actually made this herself shortly after the time in the cannon I pulled her from. It never says, though, and I really like the item, so there. >O)
*A Sword (...At least, it used to be. This is the one item Kitchel ever admits to misplacing.)
*Mini Flags (You know. Like to wave at a sporting event.)
*Her Coat (Kitchel has a white coat, rather the worse for wear after all her travels.)
*Shoes (...Kitchel has at least one pair of high-heeled boots in there. It's not clear where she got them from.)
*A LOT of Treasure (There was a literal mountain of more typical gold and jewels (and jewelry) in the caves along with the legendary Three Treasures, and Kitchel took all of it. This, added to all the other shiny stuff she picked up along the way, comprises the majority of what she's carrying around.)
[I've also added in a first-aid kit. Okay, so it doesn't actually appear in the manga, but it's not much of a stretch considering the wide range of stuff that we do see.]
The other important item that Kitchel has with her is her necklace. Given to her by Thatz at least in part so that she could work the map in the caves, it is a simple chain with a small green stone on it. It seems to be able to, in addition, protect the wearer from harm.