Community search is a personalized community discovery problem designed to identify densely connected subgraphs containing the query node. Recently, community search in heterogeneous information networks (HINs) has received considerable attention. Existing methods typically focus on modeling relationships in HINs through predefined meta-paths or user-specified relational constraints. However, metapath-based methods are primarily designed to identify single-type communities with nodes of the same type rather than multi-type communities involving nodes of different types. Constraint-based methods require users to have a good understanding of community patterns to define a suitable set of relational constraints, which increases the burden on users. In this paper, we propose FCS-HGNN, a novel method for flexibly identifying both single-type and multi-type communities in HINs. Specifically, FCS-HGNN extracts complementary information from different views and dynamically considers the contribution of each relation instead of treating them equally, thereby capturing more fine-grained heterogeneous information. Furthermore, to improve efficiency on large-scale graphs, we further propose LS-FCS-HGNN, which incorporates i) the neighbor sampling strategy to improve training efficiency, and ii) the depth-based heuristic search strategy to improve query efficiency. We conducted extensive experiments to demonstrate the superiority of our proposed methods over state-of-the-art methods, achieving average improvements of 14.3% and 11.1% on single-type and multi-type communities, respectively.