Why is that an issue for you? That is something that the apex_web_service package should handle successfully. Whether the server uses fixed content length or chunked encoding shouldn't be a concern for you.
Vanja Keglević, I have to parse JSON responses and get data from them into tables.
In case of usual response we have a naked JSON string in a response body. So it is trivial to parse it.
In case of 'chunked' we have something more complex there - and, for example, APEX_JSON.parse fails on it.
Another issue is that APEX_WEB_SERVICE can't enumerate HTTP headers in case of such response.
APEX_WEB_SERVICE.g_headers are empty.
Strange, as APEX_WEB_SERVICE package shouldn't know about that directly. What do you get as the payload from the web service in that case? What is the error APEX_JSON.parse fails with?