Hi...many Chiari specialist can tell if there is a obstruction with out a CINE if it is severe...the CINE can be used to look at things a bit more detailed..or to look for other issues...retroflexed odontoid etc....
Sometimes they do not want to take the time to see what they already know, or feel just needs to be taken care of....they r all different as to what they want or how they get that info....so, if u trust ur Drs for ur child...then u have to go with ur gut and their advisement as to what to do next.
If they can tell there is a blockage or syrinx a cine flow study is not always necessary as they are looking for a blockage. I'm sorry your daughter is suffering from chiari:( Is she seeing a chiari specialist?