With which? I think you already understand the standard way to do this. Create 25 Flat File Connection Managers and configure them to handle your 25 Flat Files. Create a Data Flow Task that loads each of the 25 files into your database tables.
If you go this route I would recommending separating this work into multiple packages. I like to keep Packages simple and doing one unit of work per. In this case I would default to 25 Packages, with each one handling one file.
There are no special teachers of virtue, because virtue is taught by the whole community.
--Plato