Motivated by the heterogeneous nature of devices participating in large-scale federated learning (FL) optimization, we focus on an asynchronous server-less FL solution empowered by blockchain technology. In contrast to mostly adopted FL approaches, which assume synchronous operation, we advocate an asynchronous method whereby model aggregation is done as clients submit their local updates. The asynchronous setting fits well with the federated optimization idea in practical large-scale settings with heterogeneous clients. Thus, it potentially leads to higher efficiency in terms of communication overhead and idle periods. To evaluate the learning completion delay of BC-enabled FL, namely FLchain, we provide an analytical model based on batch service queue theory. Furthermore, we provide simulation results to assess the performance of both synchronous and asynchronous mechanisms. Important aspects involved in the BC-enabled FL optimization, such as the network size, link capacity, or user requirements, are put together and analyzed. As our results show, the synchronous setting leads to higher prediction accuracy than the asynchronous case. Nevertheless, asynchronous federated optimization provides much lower latency in many cases, thus becoming an appealing solution for FL when dealing with large datasets, tough timing constraints (e.g., near-real-time applications), or highly varying training data.