Do I pull up mustard green if they starting to have flowers on them?

You don't have to. You can collect the seeds and plant more. The greens will be bitter once they flower.

https://bonnieplants.com/product/mustard-greens/

You can snip the new blooms off if you like and the leaves will keep producing for greens. I've done it two or three times in the past.

you can let them go and they will reseed them selves for next year.At the end of the growing season, it's actually a good idea to let plants set seed, as they may sprout from that seed the following spring. This is especially true if you don’t disturb the area where they are growing. this is good because they will naturally be accustomized to garden/climate and grow better. let them finish seeding then collect and replant next year.