Applicability of the concept of Flow-Aware Networking (FAN) for QoS assurance in wireless networks is studied in the paper. The link utilization efficiency for six versions of the TCP protocol in the FAN environment is investigated and compared. The second contribution of the paper is a new congestion control mechanism for FAN, referred to as RAMAF (Remove and Accept Most Active Flows), that fulfills the wireless link requirements. While in basic FAN, new flows cannot begin transmission in congestion, the new solution ensures short acceptance times of new streaming flows in a router regardless if the outgoing link is congested or not. As compared to other congestion control mechanisms proposed for FAN, RAMAF does not need to tune any parameters, and is thus automatic. Moreover, the proposed solution allows for more effective transmission of elastic flows in comparison to other approaches, and may be used in both wired and wireless FAN. The results of the carefully selected simulation experiments show that TCP NewJersey incorporated with the RAMAF mechanism meets the requirements of the wireless transmission in FAN.