Unchained Rogue requires you choose a weapon which functions with Weapon Finesse at lvl 3, and you gain Dex to damage with said weapon.
Double Chain Kama is a weapon I'm not certain is a Finesse weapon, however in the description it states the weapon functions as though is were a pair of normal Kama.
Assuming your unchained rogue with Finesse Training is using a double chain kama, and selected Kama as his Finesse training weapon, does he, or doesn't he receive dex to damage?
If you take Kama as your Finesse Training weapon then you would get dex to damage when using a double chain kama as two kama... but not when using it as a two-handed reach weapon.
Do not try this trick with Herolab.
Personally, I with they would errata the double chained kama to add the finesse tag.
I also wish they would give the kama, an exotic weapon, a profile at least as good as a shortsword.