The hip motion you're seeking isn't so directly affected by hip flexor flexibility. However, overall flexibility throughout the body is important for ease and fluidity of motion, subtle or grand. That said, spinal flexibility, in terms of twisting versus bending forward or back, is also a very important aspect of flexibility in ballroom dances, aiding in isolations and transitions from one position to the next.
What helped me begin to move my hips in "the ballroom way" was something an instructor pointed out. I had studied belly dance before and was so used to strict isolation of movement, I was using the wrong muscles to create movement and it never looked, or felt, quite right. My instructor reminded me to step straight back and straight forward, and as I shifted weight from one foot to the other, let the hips roll naturally (instead of allowing a deeper bend in the knee or turning out my leg, such as in ballet, to compensate.) I also had learned recently from a ballet instructor, one of the simplest things, but it made such a difference. He had said to only use just enough energy, or muscle contraction, to make the move possible.
When I combined both those thoughts and practiced my dancing, it was suddenly so easy! It all looked and felt right, and looked great as well! Hope this helps you.
