A butterfly knife trainer is a standard balisong without a blade. It is 100 percent legal in the us and, unlike a knife, you can't cut yourself.
For sharpened butterfly knives, the vast majority of states in America allow butterfly knives without any restrictions, however some states doesn't allow them, here is a list :
Puerto Rico
Guam
U.S. Virgin Islands
American Samoa
Northern Marianas
U.S. Navy vessels
Government and commercial aircraft