My answer is depends. Which is also why you are getting both yes and no answers.
Is there any law or requirement to have flotation? No.
Without float bags or other flotation in the boat, if you flip over and exit the boat, the boat will fill with some water. Depending n how little built in flotation the boat has, it is possible (but not likely) that the boat could totally sink (as in down to the bottom gone). More likely, the boat will sit very low in the water. Too low for you to be able to climb back in. But low enough that it would be hard to swim it to shore and drain it,so you might end up having to abandon it and swim yourself to safety.
So if you are paddling close enough t shore to be able to swim to safety when you flip over, then you should be Ok flotation wise. If you want to paddle further out from shore, then this boat has some safety implications.
That said, others have mentioned that this isn’t the right boat for float water paddling, and they are right. It will work in that you will float around and be able t paddle, but waiting for a more appropriate boat would give you a better experience. You may want to check out an article in California Kayaker Magazine on the different types of boats athttp://calkayakermag.com/magazine.html. Issue #10, starting at page 6.
Side note - flotation device is generally used as a term for a PFD, so when I read your subject I was wondering if you were asking about needing a PFD. The base law for the US is to have a PFD on board which is accessible and correctly sized for each person. Some local areas have more strict rules (perhaps requiring they be worn).