You can have other attacks; but they're still part of the flurry.
So a lvl 1 monk with 10 str and TWF feat and a kama in the offhand can attack at -2, -2 TWF (unarmed, kama), or -2, -2 flurrying (unarmed, unarmed) or -4, -4, -4 (unarmed, unarmed, kama). No problem.
However the same monk with...