If it's just a proof-of-concept, it may be simpler to use something embedded like sqlite's Full Text Search, than firing off requests to a different process or different server. Note that a SQLite approach won't scale (at least, not without a significant amount of forethought, planning, sharding, etc), but for a proof-of-concept it can be a good choice.
Regarding feathers.js integration, you could look at the feathers knex or sequelize modules and see if their sqlite support is helpful. That said, those kinds of query-builders are usually focused on relational database access, so I don't know if they would be helpful with Full Text Search or if they would just get in the way. You may be better off just doing it manually. While you're at it, you could look at the mongo/mongoose modules to see if they expose mongo's Full Text Search capabilities.
-- peter