The tyranids are susceptible to the physical corruption of Chaos, but the tyranids lack any semblance of emotions as we could understand it. As such, they do not feed the Chaos gods by their actions and if they are aware of the daemons or gods at all, it would be as either a threat or something to be ignored, not prey as with other life forms.
Also, the Hive Mind itself exists entirely within the warp and is channeled by the synapse creatures of the swarm. It is a reflection of the collective tyranid psyche comprised of their entire race across all the hive fleets and in between. Something of that sheer scale would not be intimidated easily, even by a Chaos god. Hypothetically, given the spread of the Shadow in the Warp that accompanies the Hive Fleets, it is entirely possible that the tyranids are as capable of feeding on warp energy as flesh. The Hive Mind's spreading influence via the shadow in the warp driving psykers insane could be an indicator that the tyranids are in fact feeding on psychic energy as they encroach, drowning out psykers and daemons alike.
Nonsense is our Salvation