Let me clarify the question: who is responsible for closing the filehandle? My code, framework (Kelp) or Plack?

Everybody is responsible :)

You assume the problem is with Kelp or Plack but you haven't ruled out your own code; you always have to rule out your own code first

If you can write a minimal Kelp app serving files that runs out of filehandles, only then can you assume there is a problem with Kelp or Plack, until then you should assume the problem is with your code

The problem is not with Kelp::Response::render_binary as it doesn't leave handles open.

It hands the handle to Plack::Response::body, and eventually sub response_cb in Plack::Util which reads from the handle and then closes the handle.

On a side note, if don't already know, you should ignore flushells the troll

Questions of this nature can be pretty-much categorically answered:   “it must be You!”

• “Plack is a plumber,” solely responsible for getting a request delivered from Apache to you, and a subsequent response delivered from you to Apache.   No smoking-gun here...
• Kelp, likewise, is a framework:   “generically” engineered to taking care of “whatever is ‘generic,’” so that you don’t have to.
• ... which leaves:   you.   Your application must be prepared to handle many (thousands of?) requests without “leaking.”   (It can, to a certain extent, “take the easy way out” by asking the PSGI manager to arrange for you to “commit hari-kiri” after so-many requests, but that is a crutch.)   You should always assume that you are responsible for closing all resources.