The bottleneck of distributed edge learning (DEL) over wireless has shifted from computing to communication, primarily the aggregation-averaging (Agg-Avg) process of DEL. The existing transmission control protocol (TCP)-based data networking schemes for DEL are application-agnostic and fail to deliver adjustments according to application layer requirements. As a result, they introduce massive excess time and undesired issues such as unfairness and stragglers. Other prior mitigation solutions have significant limitations as they balance data flow rates from workers across paths but often incur imbalanced backlogs when the paths exhibit variance, causing stragglers. To facilitate a more productive DEL, we develop a hybrid multipath TCP (MPTCP) by combining model-based and deep reinforcement learning (DRL) based MPTCP for DEL that strives to realize quicker iteration of DEL and better fairness (by ameliorating stragglers). Hybrid MPTCP essentially integrates two radical TCP developments: i) successful existing model-based MPTCP control strategies and ii) advanced emerging DRL-based techniques, and introduces a novel hybrid MPTCP data transport for easing the communication of the Agg-Avg process. Extensive emulation results demonstrate that the proposed hybrid MPTCP can overcome excess time consumption and ameliorate the application layer unfairness of DEL effectively without injecting additional inconstancy and stragglers.