Learning Healthcare Systems are an emerging approach to healthcare research as translated into practice. For this purpose, a strong interconnection comes to be a necessity when dealing with healthcare services, research and knowledge transfer all at once. Practically, these connections imply that a routing protocol should guarantee anonymity to entities in compliance with both laws and ethical requirements while restricting the quantity of information obtainable had an entity been compromised. In order to bring more protection and meet all the requirements, a new message routing protocol is offered to allow the use of data access paths and to resist traffic analysis security threats. The protocol protects the addresses and roles pertaining to entities from any lurking malevolent minds by implementing proxies into a mix-network. Moreover, flows of synthetic datasets and contents identifiers are handled separately so as to curb any risk of re-identification. A model of this protocol is provided in the form of a multi-objective optimization problem, natively integrating objectives of minimizing both latency and entropy of the information exchanged. The assessment of this model shows that the constrained separation of data flows has a minimal impact on delay times, which not only reveals to be an acceptable compromise but also significantly increases security in data access.