Chinampas and floating fields are possible in many places. In the Amazon and similar riverine systems, the issue in water current, especially during annual floods and intermittent rainfall and snow melt events. You don't want to watch all that work go floating away. You could circumvent some of this problem by locating your fields away from the worst areas of current, on higher ground flooded only by shallow waters, or use of strong enclosures/embankments/levees. You have much less of a problem in lakes, ponds and marshes. In the case of smaller streams, you could place the fields off the main flow in natural of man-made marshes. The problem is not insurmountable if you have large amounts of labor, free time and patience.
Edit: This would be a great complement to Terra Prieta.
Hmmm... interesting.
Would't that recquire a pre-existing level of organization through? Seems like something that the Marajoarans and the builders of Kihukigu could make, but not your average tribe