Open a stream, and use teh
Read[
^] method to fetch a chunk of data. That's the simple bit.
Adding it to the DB is the difficult part: unless you are reading text from the file, you can't "append" the data into a DB column (and even with text, that would be monumentally inefficient), so you would have to assemble all the chunks into a single "block" to send it to the DB anyway. And if you are doing that, you might as well just use File.ReadAllBytes to get the lot and pass that to the DB in the first place.
The only time when this is really silly is when your file sizes start to get huge - and if you are storing huge files in your DB then that's probably a major mistake anyway!