If this behavior is out of the blue and atypical, take her to a child psychiatrist for play therapy to make sure nothing bad happened to her to trigger such a violent reaction all of a sudden. If she’s in a preschool, camp or daycare, talk to her teachers about what they see and how they would handle the situation.
If not, and maybe you’re in for more of this type of behavior as she’s reached this new phase, teach her words to express herself, (“Do you feel sad, mad, frustrated or tired?”) and sympathize with her (“I understand you are mad I said no. It’s hard sometimes to not get what you want when you want it and it doesn’t feel good, does it?” “Do you think yelling and kicking is likely to change m mind?” “Are you having a bad day and this is just the final thing that sent you over the edge?” “Some days are harder than others, aren’t they?”
During calmer times teach her methods she can use to calm down and get herself under control. Deep breaths, visualization, meditation, sitting in the car by herself and screaming, watching cat videos—ask friends and professionals what they recommend at this age. Practice these techniques together when calm, and pull them out early in the tantrum phase.
Tell her when she’s calm you and she can find solutions together. E.g. “We can’t get this book now, but let’s see if they have it at the library tomorrow.” “If you really want that book, maybe you could take on some tasks and earn the money to pay for it.” “If the store is too loud and distracting for you, maybe you’d prefer to stay home with Dad next time while I shop.” “If you feel you are getting really upset, let’s come up with a signal so we can leave before you blow up.”
Work hard to stay calm yourself and tell her you are both going to take some time out until it’s easier to talk it out and solve problems. Ask her if she would rather go for a walk, sit in the car, or run or jump up and down the sidewalk or wherever it might be safe to do so to help get her frustration out and calm down. Might be good to have a pillow handy she could punch.
Good luck. Make sure she gets adequate sleep, nutrition, vigorous exercise and fun.