How do you know if you've been blocked from someone's facebook chat?

If you cannot see some, or all, of their content such as wall, images, updates, etc. No app can tell you who blocks you. Those are scams to collect personal information and sometimes viruses/malware.

Below is from Facebook:

If you block someone, they will not be able to find you in a Facebook search, see your profile, or interact with you through Facebook channels (such as Wall posts, Poke, etc.). Any Facebook ties you currently have with a person you block will be broken (for example, friendship connections, Relationship Status, etc.). Note that blocking someone may not prevent all communications and interactions in third-party applications, and does not extend to elsewhere on the internet.

(this is straight from facbook.com under the privacy settings)