Next-generation Wi-Fi networks are looking forward to introducing new features like multi-link operation (MLO) to both achieve higher throughput and lower latency. However, given the limited number of available channels, the use of multiple links by a group of contending Basic Service Sets (BSSs) can result in higher interference and channel contention, thus potentially leading to lower performance and reliability. In such a situation, it could be better for all contending BSSs to use less links if that contributes to reduce channel access contention. Recently, reinforcement learning (RL) has proven its potential for optimizing resource allocation in wireless networks. However, the independent operation of each wireless network makes difficult -- if not almost impossible -- for each individual network to learn a good configuration. To solve this issue, in this paper, we propose the use of a Federated Reinforcement Learning (FRL) framework, i.e., a collaborative machine learning approach to train models across multiple distributed agents without exchanging data, to collaboratively learn the the best MLO-Link Allocation (LA) strategy by a group of neighboring BSSs. The simulation results show that the FRL-based decentralized MLO-LA strategy achieves a better throughput fairness, and so a higher reliability -- because it allows the different BSSs to find a link allocation strategy which maximizes the minimum achieved data rate -- compared to fixed, random and RL-based MLO-LA schemes.