Ask Mr. Smarty Plants

This recent Mr. Smarty Plants answer from San Jose CA has the same concerns you do. While that question was more specific in the area that would be enclosed by concrete than you did, you can certainly read the rest of the article re: non-invasive roots, which you probably asked for with the same reason in mind. Of the list we gave on that answer for Santa Clara County in Central California, these shrubs are also native to the area of southwestern Los Angeles County:

Amelanchier alnifolia (Saskatoon serviceberry)

Arctostaphylos pungens (Pointleaf manzanita)

Cornus sericea (Redosier dogwood)

Fremontodendron californicum (California flannelbush)

Quercus douglasii (Blue oak)

In particular, follow these instructions for finding plants for your area:

"If you have difficulty finding the California native plants you select, go to our National Suppliers Directory, put your town and state or just your zipcode in the "Enter Search Location" box and you will get a list of native plant nurseries, seed companies and consultants in your general area. All have contact information so you can inquire in advance whether they have what you are looking for."

You will probably find Las Pilitas Nursery on that list, because it is also in Southern Caifornia, as are you. It has two locations and specializes in plants native to California. In addition to being convenient, they probably have a better selection of plants for your area than we do in our Native Plant Database.

And one other thing - you asked for flowering trees. That is easy: all trees bloom, as do all other vascular plants, native or not. It is necessary for the process of propagation, they must bloom, attract pollinators, form seeds and drop them to the ground in order to perpetuate themselves, which is what all plants are required to do.