Is this the plant's first bloom? If it is, the stems will often stay curled instead of bearing themselves upright, and that may fix itself on the next blooming. Keep in mind though that some Paphs don't grow their flower stems upright, but rather leave them curly so that the flower flops over. Do you know what kind of Paphiopedilum you have?
Regardless, most Paphs, if their spikes are left alone without being staked, will not hold their flowers straight up and down, but will keep them hunched forward so that the dorsal sepal covers the pouch and keeps water from entering. If you want the flower to face you squarely when it opens, you're going to have to carefully tie or clip it to the support stick you mentioned.