We calculate the hypertriton binding energy and the \(\Lambda d\) and \(\Sigma d\) scattering lengths using baryon-baryon interactions obtained from a chiral constituent quark model. We study consistently the \(\Lambda NN\) and \(\Sigma NN\) systems analyzing the effect of the \(\Sigma \leftrightarrow \Lambda\) conversion. Our interactions correctly predict the hypertriton binding energy. The \((I,J)=(0,3/2)\) \(\Lambda NN\) channel is also attractive and it might have a bound state. From the condition of nonexistence of a (0,3/2) \(\Lambda NN\) bound state, an upper limit for the spin-triplet \(\Lambda N\) scattering length is obtained. We also present results for the elastic and inelastic \(\Sigma N\) and \(\Lambda N\) cross sections. The consistent description of the \(\Sigma N\) scattering cross sections imposes a lower limit for the corresponding spin-triplet scattering lengths. In the \(\Sigma NN\) system the only attractive channels are \((I,J)=(1,1/2)\) and \((0,1/2)\), the \((1,1/2)\) state being the most attractive one.