Hi
Shoulder flexibility in no way! can effect hip flexibility. The reason for this is, is that flexibility is joint specific. You cannot say. or more like its very unaccurate to say someone is flexible just because they can do the splits for example. Because just because at the same time they might not be soo stiff in the shoulders that they can't even scratch their back, or raise their arm over their head, or extend their knees to a full 180, or squat with the heels coming of the floor...etc..
"It seems like a lot of people with shoulder flexibility problems also have tight hip flexors"
Big generalisation this one, because you might want to consider the people you are thinking about. In gymnastics a great deal of emphasis is placed on Hip flexibility, to the point that shoulder flexibility is sometimes neglected, or in most cases its just never worked as hard as hip flexibility. Consider the people you are thinking about and their daily activity, sport, lifestyle, job ect. Someone stuck at the computer 24/7 for example will develop flexibile extensors (trunk) and develop tighter hip flexors, simply because a great deal of time these muscles are spending in extended and flexed positions. So i personally would not agree to say that a lot of people do exibit this, but i would agree that in general, people are not very flexibile, as a result (in my opinion) due to the more and more sedentry lifestyles we live. Also there is still not enough emphasis on flexibility work on most sports/rec activies.
"I can easily kick my foot over my head using mostly lower back flexibility, "
The ability to dynamicly swing a limb through a certain range of motion (ROM) is an example of dynamic flexibility. The ability to move a limb though a ROM and sustain it at the exteme end of the ROM is an example of active fleixbility. The two are moderately correlated, but are definitely not the same thing, and require sperate modes of training.
When you say you can kick your leg over your head (as you see Ruthmic gymnasts do during warm-ups).. i am thinking one of two ways.. either in like a scopion kick thing..where you are like on all all fours (4 point stance), or a similar position and you swing your leg. OR from standing you are kicking it infront of you. Its important to clarify because the ROM you are exibiting is controled/limited by opposing muscle groups. When you say you arch in your back i am thinking that you are doing the first option. Even though you arch in your back (due to joint anatomical reasons most likely, as the joint is not actually capable of doing such a thing (even though in some cases due to joint deformation it would/might be possible). So arching helps you to put the joint in a position to be able to do it this, and maybe you bend in the knee as well. If this is the case you actually ahve some pretty flexibiluty hip flexors haha..
The shoulders are just not involved in this.
"I could never pull my foot up there and hold because of my shoulders (and prob hip flexors if that makes sense)"
To be honest i dont quite understand what you mean, as in, in what position are you doing this?
But regardless as i mentioned before this is because you are testing 2 different kinds of flexibility, and even though you sound like you have developed pretty awesome dynamic flexibility, your active flexibility is not as well developed. It means you with the help of momentum can achieve take the joint though this set ROM, but your muscles are not stron enough to take the leg though this. One thing that definitely can be generalised is that active flexibility is almost always neglected and trainined minimaly. Even though in some sports this not the case (takewondo being on that definitely works on developing it).
I hope that answers some of your questions.