I suspect the problem is gzip-ing the output. (Your working nginx server is not doing that.)
In your .htaccess file, can you try both of these:
php_flag zlib.output_compression off SetEnv no-gzip 1
(Borrowed from https://webmasters.stackexchange.com/q/61258/18151 and its answers.)
BTW, you shouldn't need to add the chunking header yourself; it will be set if the output is chunked.