Chicory usually flowers in its second year, and then continues every year after that. If you’re harvesting the roots, perhaps you’ve been removing them before they got to that age? Maybe set aside a few plants for greens only and allow those to develop roots undisturbed - they’ll probably flower before long.
They grow great up here in NorCal, all the roadsides are completely covered in them every year. You’re a little hotter and drier down there, but if the basal rosette is doing well, the plants should be fine.
I think you’ve solved the mystery @graysquirrel, I was a little impatient last year and dug up the roots before replanting from seed again this year. They definitely thrive here if grown out of direct sunilight.