Yesterday, I emailed Kino, asking her for her opinion on the relative merits of jumping through with straight legs versus jumping through with crossed legs. She has very generously and speedily replied to my email with her thoughts on this matter. With her permission, I will share her thoughts below. I hope you will find this to be of benefit to you in your practice. This is what she says:
"Jumping through with crossed legs or bent legs can both be very beneficial. One is not more correct than the other. In fact a student once asked R. Sharath Jois why he does not jump through with straight legs in his DVDs, to which he said, "Never bothered to learn." Different students may find different benefits from each method at different times in their practice. For example, many students want to learn how to jump back and jumping through with crossed legs helps build the neurological patterning and strength needed to reverse the movement and jump back. The most common way to jump back is with crossed legs so in order to practice jumping back it just makes sense to jump through with crossed legs too. While on the other hand if you want to learn how to more easily move into a deep forward bend or perhaps give yourself a lighter jump through to rest between certain very challenging postures the straight leg jump through may be best for you. Either way what often happens when students become habituated with the movement of jumping through is that they often do not pay careful attention to each step. Make sure that whichever method you choose you keep your hands planted firmly on the ground the whole time, that you create a solid structural foundation through the upper body, that the pelvis is aligned so that both legs are involved in the motion equally and that you control the landing with as much grace and ease as possible."