Here is what the US Coast Guard has to say:

(ii) A vessel under oars may exhibit the lights prescribed in this rule for sailing vessels, but if she does not, she shall exhibit an all around white light or have ready at hand an electric torch or lighted lantern showing a white light which shall be exhibited in sufficient time to prevent collision. Vessel Under Oars

A 360 strobe has obvious utility, but also is likely to blind the kayaker while performing its function. I'll stick with a headlamp, not just the brand i prefer, but many of the other brands sport variable light levels and reasonable waterproofness (Fenix, Nitecore et al.)

Kayaking at night in the presence of other craft seems like a bad idea. I have always been on shore watching the sunset.... I carried a signal mirror and flares for day time emergencies