There is increasing adoption of machine learning to encode data into vectors to serve online recommendations and search use cases. As a result, recent data management systems propose to augment query processing with online vector similarity search. In this paper, we explore vector similarity search in the context of Knowledge Graphs (KG). Motivated by the tasks of finding related KG queries and entities for previous KG query workloads, we focused on hybrid vector similarity search (hybrid queries for short) where part of the query corresponds to the vector similarity search and part of the query corresponds to predicates on relational attributes associated with the underlying data vectors. For example, given previous KG queries for a song entity, we want to construct new queries for new song entities whose vector representations are close to the vector representation of the entity in the previous KG query. But the entities in a KG also have non-vector attributes, such as a song associated with an artist, a genre, and a release date. Therefore, suggested entities must also satisfy query predicates on non-vector attributes beyond a vector-based similarity predicate. While these tasks are critical to KGs, our contributions generally apply to hybrid queries. Unlike previous work optimizing inline queries, we focused on enabling efficient batching of earlier hybrid query workloads. Introducing our system, HQI, for high performance batch processing of hybrid queries. We present a workload-aware vector data partitioning scheme to tailor vector index design to the given workload and describe a multiple query optimization technique to reduce the overhead of vector similarity calculations. We tested our methods on industrial workloads and demonstrated that HQI yields 31 Performance improvement for finding related KG queries compared to existing hybrid query processing approaches.