The timed text metadata isn't stored in the m3u8 file as suggested by Nikola's answer, but instead stored in the mpeg2 ts segments. An overview of how it's embedded in the ts is available here: https://developer.apple.com/library/ios/documentation/AudioVideo/Conceptual/HTTP_Live_Streaming_Metadata_Spec/HTTP_Live_Streaming_Metadata_Spec.pdf
You can try extracting the metadata with ffmpeg, the command should be something along the lines of this:
ffmpeg -i in.ts -f ffmetadata metadata.txt
You'll need to do the equivalent using jni and libavformat. It's not incredibly easy, and you'll still need to come up with a mechanism for signaling the read metadata to your application.
If you can, I would recommend signaling the timed metadata via a separate mechanism. Could you extract it and put it as a text file that your player downloads separately? Then you lines up with the timeline as reported by the video player? That would be much simpler to implement, but I don't know your requirements.