BNC heteronanotubes are promising materials for the design of nanoscale thermoelectric devices. In particular, the structural BN doping pattern can be exploited to control the electrical and thermal transport properties of BNC nanostructures. We here address the thermoelectric transport properties of (6,6)-BNC heteronanotubes with helical and horizontal BN doping patterns. For this, we use a density functional tight-binding method combined with the Green's function technique. Our results show that the electron transmission is reduced and the electronic bandgap increased as a function of the BN concentration for different doping distribution patterns, so that (6,6)-BNC heteronanotubes become semiconducting with a tunable bandgap. The thermal conductance of helical (6,6)-BNC heteronanotubes, which is dominated by phonons, is weakly dependent on BN concentration in the range of 30-80%. Also, the Seebeck coefficient is enhanced by increasing the concentration of helical BN strips. In particular, helical (6,6)-BNC heteronanotubes with a high BN concentration (>20%) display a larger figure of merit compared to other doping distributions and, for a concentration of 50%, reach values up to 2.3 times and 3.4 times the corresponding values of a CNT at 300 K and 800 K, respectively. Our study yields new insights into the parameters tuning the thermoelectric efficiency and thus provides a starting point for designing thermoelectric devices based on BNC nanostructures.