Is this possible? Will be flying from Havana to Baracoa and then from Santiago de Cuba to Havana in June and July.

US credit cards do not work in Cuba. They are blocked by the banks. Banks believe they will be fined if they don't block their use in Cuba.
Thanks. But I can book and prepay for other services with US cards from the US, such as casa particulares (through airbnb, etc.). I've heard that this might be possible for airlines, too, maybe through an intermediary. I know I can't use my cards while in Cuba.
I believe that Cubana's website might route payment through a Spanish company. Or look at Cubajet.com which is part of Cuba Travel Services.
I don't know about once you are in Cuba.
(Of course, some US cards, such as Stonegate, do work in Cuba).

I have been booking cars through a contact i have in Havana for quite a few years. The last time was at the very end of last year. No cars available through any website. He found me two. Held them for 5 days to let me decide which one i wanted to rent.
Ya, payment is made through a Spanish website, if i recall. He sends me a link, specific to my booking. It's good for 24 hrs. I pay, using my credit card, he sends me the voucher. Never had a problem. In my case, it's not a US credit card but he has told me to keep it quiet and not blah blah about it on the internet. I can mention it since I am not giving any details.
They do accept US credit cards but it's, somewhat, esquierda and he doesn't want it shut down.
I use him because he has always been able to find me multiple cars when no one else could. Prices were rack.
He also books hotels, guides, you name it. I assume, flights also. No cp,'s.
He used to post here a few years ago until they, basically, banned him.
No, don't ask me for his email if you are from the USA. I won't give it even though i would like to steer more business his way.
Just saying, yes there are Cuban entities that you can book services using a USA credit card.