Why can Qiaozui Zhang use gold hairpin?

Because she knows the formula. According to the plot query of the TV series "The Fairy Couple", Jin Chai was originally the magic weapon of the Queen Mother. The golden hairpin made of gold is a portable headdress. This treasure has infinite magic power and was given to the seven fairies. Later, it was stolen by Qiaozui Zhang. Because Qiaozui Zhang knows the formula to drive Jin Chai, she can also use it.