Where do websites like expertflyer.com get their information?
Simply put, ExpertFlyer gets its data from purchasing it from the GDSs (global distribution systems for airlines) these are the same systems that travel agents (online and off) use to book tickets/travel for their customers. This has a cost but has advantages vs free but less reliable means of acquiring flight data.  

Other services may screen scrape (take) information from public airline websites, however airlines frown upon that. We have seen active campaigns by airlines to go after services that collect data in this manor.

Please note, this post is not meant to be "promotional" however fully answering the question posed requires explaining how different services may acquire flight data. Also, if the name "ExpertFlyer Voice" didn't indicate to you, I am a representative of ExpertFlyer.com