It would certainly be one of the factors affecting it, but not the only one. For example, temperature is also known to affect righting time, as is stress (Lawrence & Cowell 1996). These effects probably mainly influence the speed of muscle movement, whereas flexibility would more likely affect the likelihood of an attempt to right itself being successful - so, a different process.

John M. Lawrence , Bruce C. Cowell, 1996. The righting response as an indication of stress in stichaster striatus (Echinodermata, asteroidea). Marine and Freshwater Behaviour and Physiology, Vol. 27, 239-248.

Thank you Sir Joseph!

On the west coast of Canada we have many shallow water sea stars and they vary greatly in terms of righting time. Luidia foliolata is a large five-rayed species reaching 40 cm in diameter, yet it is extremely flexible and can right itself in less than 30 seconds. Pycnopodia helianthoides is a very large, soft-bodied star that is also very flexible with a relatively quick righting response. Stars that are much more rigid and with shorter rays such as Mediaster aequalis and Ceramaster patagonicus, take considerably longer to right themselves as they do not have the advantage of longer rays to provide flipping leverage. So to answer your question I think righting time in stars depends on a number of physical factors, including size, relative length of rays and overall flexibility (which can change quickly due to their catch connective tissue).

I have also worked with a number of the west coast species in Canada. I believe the density, surface area, and length of podia is another a contributing factor in right times.