This is technically a two part question. For the sake of this question assume that the PC is not a Monk or already proficient with "all Monk weapons" by some other means.
Description of the Double-Chained Kama from d20pfsrd for reference:
The wielder can attack as if armed with a single kama in each hand or extend the chain to make a single reach attack. By swinging the rope, the wielder can whip the kama about to disarm or trip opponents. Furthermore, if one of the weapons is dropped, the wielder can retrieve as a free action by pulling on the chain.
- If you are somehow proficient with the Double-Chained Kama (ie EWP feat or Weapon Familiarity custom race trait), are you considered proficient with Kamas when using each side as a single Kama?
- If you are proficient with the Double-Chained Kama, are you considered proficient with the single Kama as well?
Note: Both are Exotic weapons.