The RAW is unclear.

The rules for flurry say you can only use monk weapons "when using flurry of blows". The murky part is the rules never really specify when exactly flurry starts, ends, or what happens to attacks that you make "outside" of the flurry. If you get another attack via a different ability/feat, does that attack still have to follow the rules for a flurry, or can it happen "after" your flurry attacks? RAW doesn't say, so you'll have to discuss with the DM what works best for your game.

If you want a RAW work-around, you can take Unorthodox Flurry (Dragon Compendium) for each of your natural weapons, which allows them to be considered monk weapons.