Somewhat surprisingly, there is an American Eagle flight MQ9513 from Havana, Cuba to Miami, Florida. Here is a photo I took of an arrivals monitor in MIA showing the flight has landed.

And, checking Flightstats.com, I can see that the same flight came in today to Miami from Havana:

So how do you book this flight?
If I do a search for a flight from Havana to Miami on Google, I see this:

So far, so good. So, what happens if I click on the Expedia link near the top there?
I see this:

When I click on the Orbitz link, I see "We're sorry, Orbitz does not support flights that originate from Havana, Cuba(Message 1031)".

Travelocity says "Unfortunately, no flights met your search criteria for the airports you selected. Possible Causes: * This could be a peak travel time for your destination. * Your search may have been restricted by airline, stops, fare class, or fare type."
When I click on Priceline, even the PriceLine Negotiator has to give up and says "We are unable to find flights that match your exact criteria. We recommend that you try another search using different dates, locations or options if you can."
So is it possible to book that flight? Hmm.....