A Note on Kits

Kits are a way to help make a character different from all the other characters of the same class. Kits extend advantages and disadvantages to the character, and form an outline for customizing a character.
Although there are separate kits for demihumans and subclasses (druids, necromancers, etc.), demihuman races and subclasses may take any of the kits listed in the four basic handbooks (fighter's, rogue's, priest's, and wizard's). They are not restricted to the kits listed in their individual handbooks.

Warrior Kits and Multi-Class Characters

These Warrior Kits are designed to add depth to a warrior-class character. But if the character is already multi-class (for example, an elf fighter, mage), he doesn't need any more depth. Therefore, only single-class warriors can take one of the Warrior Kits from the Fighter's Handbook.
However, with your DM's permission, there's no reason why a multi-class warrior can't use his weapon and nonweapon proficiency choices to simulate one of the Kits... and, again with DM permission, the characters possessing that Warrior Kit gan consider him "one of their own" within the context of the campaign.
For example, let us say that your campaign features an elvish Amazon tribe and you want to play an elf fighter/thief who belongs to that Amazon tribe.
Build her this way: Have her take Spear and Long Bow Weapon Proficiencies. For her Non-weapon Proficiencies, have her take Riding (Land-Based) and Animal Training (she doesn't get either of these for free, like the "real" Amazon, but she can still choose them). For her Equipment, limit her to the equipment choices of the Amazon.
If you do all this, and have your DM's permission, within the context of the campaign, your character will be considered an Amazon. That is, she comes from the Amazon tribe and the other Amazons consider her to be a shield-sister and one of their own. You know, and the DM knows, that she doesn't have all the special benefits of the Amazon Warrior Kit. And the DM is within his rights to assign the character the special hindrances of the Amazon — after all, you •ve chosen for her to be identified with a race of people with those hindrances. But to all outward eyes, she is indistinguishable from any other elvish Amazon.

Warrior Kits and Dual-Class Characters

The same is not true of dual-class characters.
If a character starts off as a warrior. he may take any of the Warrior Kits above. If, later, he decides to change classes according to the normal Dual-Class Benefits and Restrictions rules, he doesn't lose any of the benefits or hindrances of the Kit he chose; he is still that sort of fighter. If that second character class also has a range of Kits available to it, he may not choose a new, additional Kit.
If a character starts off as some other character class, does not take on a Kit appropriate to that class, and then later switches to one of the warrior classes, he can choose a Warrior Kit at that time... though the DM may insist that certain campaign events be accomplished in order to allow him to do this.
For instance, let's say that a human mage decides, later in life, to become a Fighter, and he wants to be a Gladiator. Well, there's nothing wrong with that. But the DM should insist that the next several adventures deal with that transformation. The character must be hired by (or, alternatively, captured and enslaved by) an arena or fighting-stable owner, trained, and pitted against other Gladiators. The other characters in the campaign could also be entering the gladiatorial arena, or the DM could contrive things so that the current adventure involves gladiatorial elements and still get all the PCs involved, better simulate the wait involved for the character to learn his new trade, the DM is within his rights to insist that the character not receive his Warrior Kit until he's reached second experience level in his new class.

Abandoning A Kit

Sometimes it happens that a character is created with a Warrior Kit and circumstances later force him to reconsider his character's role.
For example, a Noble Warrior could become disgusted with the corruption and excesses of his class and decide to renounce his ties to the nobility. Or, a Savage could become increasingly comfortable with the civilized world and increasingly uncomfortable with his savage kin. In such a case, the player should think about abandoning the Warrior Kit.
To abandon the kit, the player should privately tell the DM his intentions. If the DM has no objections to the abandonment, then it will take place. Unless the choice for abandonment were brought on by a sudden, traumatic event, the DM may have to have some time to work the abandonment into the storyline. Often, in the story, the character doing the abandoning will have to role-play out the situation: Publicly renounce his ties with the others of his Warrior Kit, and then suffer any consequences that might arise. (In Greek mythology, for instance, the Amazon queen Antiope abandoned her former life to stay with King Theseus of Athens... and she later died fighting her former countrywomen when they came after her.)
Once the character abandons his kit, he also abandons all the special benefits and hindrances it provides. Often, those benefits included free Non-weapon Proficiencies or Weapon Proficiencies. The character doesn't lose those, but he must pay for them from the next free slots he has available to him.
The character may not take another Warrior Kit to replace the one he's abandoned. Once he gives up his Warrior Kit, he's an ordinary Fighter, Paladin, or Ranger for the rest of his playing life.