How would you build a database filesystem (DBFS)?
DBFS is a really nice PoC implementation for KDE. Instead of implementing it as a file system directly, it is based on indexing on a traditional file system, and building a new user interface to make the results accessible to users.
I'm not really sure what you mean with "A database file system is a file system that is a database instead of a hierarchy".
Probably, using "Filesystem in Userspace" (FUSE), as mentioned by Osama ALASSIRY, is a good idea. The FUSE wiki lists a lot of existing projects about databased-backed filesystems as well as filesystems in which you can search by SQL-like queries.