If we say he has no right to do so then none as the right to read the bible or follow it because everything he said was in it and since we where kids we where told the bible say's the truth and no lies.
This has been extensively discussed on this forum already, but you generally have no notion of freedom of speech w.r.t. to work. What that means is that people can and do get fired for saying their religious beliefs, or just about anything. The general (and probably most appropriate) interpretation is that no-one can stop you from saying what you want, but there can be repercussions to doing so. Freedom of speech doesn't exempt you from repercussions for your words.
More strictly speaking, freedom of speech as written in law deals primarily with the government interference to your freedom of speech. In short, it essentially says that the government can't make laws inhibiting your freedom of speech. It doesn't make any statements about other individuals or businesses taking actions against you for what you do say.
From a religious standpoint, laws do say that employees aren't allowed to be persecuted for religion/etc. This is true, but making religious speech (or any speech) in a work context isn't covered by the law. The applicable difference is that you can't be fired simply because of your religion, but you can be fired for preaching it or talking about it (the reason could be as simple as, he/she was distracting other workers -- notice how the reasoning isn't actually related to religion). In the case of Duck Dynasty, the reason could simply have been that his contract listed that he not make controversial statements that upset the network viewership. In reality, I'm sure his contract listed that he could be terminated for any reason at any time.