VLC for Kindle plays most local video and audio files, as well as network streams (including adaptive streaming), like the desktop version of VLC.
VLC for Kindle has a media library for audio and video files, and allows to browse folders directly.
VLC has support for multi-track audio and subtitles. It supports auto-rotation, aspect-ratio adjustments, hardware acceleration and gestures to control volume.
It also includes a widget for audio control, supports audio headsets control, cover art and a complete audio media library.