In location-based services(LBSs), it is promising for users to crowdsource and share their Point-of-Interest(PoI) information with each other in a common cache to reduce query frequency and preserve location privacy. Yet most studies on multi-user privacy preservation overlook the opportunity of leveraging their service flexibility. This paper is the first to study multiple users' strategic cooperation against an adversary's optimal inference attack, by leveraging mutual service flexibility. We formulate the multi-user privacy cooperation against the adversary as a max-min adversarial game and solve it in a linear program. Unlike the vast literature, even if a user finds the cached information useful, we prove it beneficial to still query the platform to further confuse the adversary. As the linear program's computational complexity still increases superlinearly with the number of users' possible locations, we propose a binary obfuscation scheme in two opposite spatial directions to achieve guaranteed performance with only constant complexity. Perhaps surprisingly, a user with a greater service flexibility should query with a less obfuscated location to add confusion. Finally, we provide guidance on the optimal query sequence among LBS users. Simulation results show that our crowdsourced privacy protection scheme greatly improves users' privacy as compared with existing approaches.