Fly direct is correct, although fly directly is technically correct as a verb + adverb construction, but people use fly direct to mean that there are no changes. Fly directly has more shades of meaning, like for example when someone is in a rush, or there is some urgent business to be sorted out. So fly direct is just a neutral phrase that describes a type of flight.

Thank you dear Jerry~

Jan is correct. I would just add that this is the term that the airlines use. A 'direct flight to Houston' for example. So this is what we say in real life.