A miracle of the Prophets is by definition inimitable because it defies the natural laws and it is exclusive to the Prophets.
"Learning" the language of the birds or at least understanding it still does not come close to the miracle granted to Sulayman (as) because he was
given the ability to fluently converse with the birds and understand the language of other creatures such as ants. He was given command over the wind and the jinn. All these are from the miracles granted to him which will never come to anyone else after.
As for talking and communicating with Jinns, then it is already possible but prohibited because it is done via black magic and black magic is automatic disbelief. People that exorcise jinns do in fact speak to the jinn and the conversations have been recorded. You can read about one such event here:
http://muslimmatters.org/2008/02/11/a-conversation-with-a-jinn-the-exorcism-experience/
As for the Qur'an, then it can never be imitated, which I say by way of educated belief and not just blind faith Alhamdullilah. It is simply beyond the capability of a human being to produce something like it.