Knowledge Graph Embedding (KGE) is a fundamental technique that extracts expressive representation from knowledge graph (KG) to facilitate diverse downstream tasks. The emerging federated KGE (FKGE) collaboratively trains from distributed KGs held among clients while avoiding exchanging clients' sensitive raw KGs, which can still suffer from privacy threats as evidenced in other federated model trainings (e.g., neural networks). However, quantifying and defending against such privacy threats remain unexplored for FKGE which possesses unique properties not shared by previously studied models. In this paper, we conduct the first holistic study of the privacy threat on FKGE from both attack and defense perspectives. For the attack, we quantify the privacy threat by proposing three new inference attacks, which reveal substantial privacy risk by successfully inferring the existence of the KG triple from victim clients. For the defense, we propose DP-Flames, a novel differentially private FKGE with private selection, which offers a better privacy-utility tradeoff by exploiting the entity-binding sparse gradient property of FKGE and comes with a tight privacy accountant by incorporating the state-of-the-art private selection technique. We further propose an adaptive privacy budget allocation policy to dynamically adjust defense magnitude across the training procedure. Comprehensive evaluations demonstrate that the proposed defense can successfully mitigate the privacy threat by effectively reducing the success rate of inference attacks from 83.1% to 59.4% on average with only a modest utility decrease.