Diamond Embers by Jadyn Chase

At an ultra-secret military base in Antarctica, Project: Reborn Fire has succeeded in creating genetically engineered dragons to serve as the perfect all-purpose weapons.
The Sapphire, Obsidian, and Diamond dragons are all beautiful and deadly. But the plan goes astray when the dragons, built in part from human DNA, begin to show a chameleon-like ability to fully change their shape and appear as men.
Then, in a single night, the project is lost entirely when an asteroid strike sends the world into an apocalyptic nightmare. After that, the powerful dragons establish rule over the ruined planet.
The Diamond and his devoted scientist, Dr. Rose Morgan, leave the Antarctic base along with the Diamond clones and their female humans. They find a sheltered tropical beach where they will rebuild their lives.
But Rose and the other women quickly learn that when in human form, these Dragonmen – strong and handsome and protective as they are – also have the cold and distant personalities of their dragon sides. They compete viciously with each other for leadership and have little concept of love for their females.
If they hope to find not mere survival with their dragon mates, but real love and a new life worth living, Rose and the other women must somehow reach the human side of their Dragonmen – but that could be a very dangerous task, if not an impossible one.