Depending on which wildflowers you decide on, many wildflowers bloom in the spring when the grass is nice and green and like grass die off in the summer.
Perennial flowers might work if you make a perennial flower bed.
I have a butterfly garden with blue sage and mealy blue sage that works well without water. I like to plant sweet alyssum as a ground cover though that will need water.
Though most plants that are drought resistant don't have shallow roots as the seep roots are what make the drought-resistant.
This thread is about a different situation than what you are suggesting though some of the flowers mentioned might work for you:
https://permies.com/t/142667/Wildflower-Meadow
This is another interesting thread:
https://permies.com/t/1760/grow-neat-stuff-lawn