I’d say that he’s unmarried. Bhadra is adopted.

Reasons

1. Bhallaldev is not at all emotional or sad about Bhadra’s death. Yes he vows revenge, but holding his son’s decapitated head should evoke more emotion than mere frustration.
2. Amrendra’s son, Mahendra, is as strong and skilled and intelligent as he is. And both characters played by Prabhas.. . . Bhadra is nowhere near as powerful as bhallaldeva. And he’s killed way too easily, that too while fleeing.
3. Even bijjaladeva didn’t show emotions when his grandson was killed. And mind you, bijjaladeva was highly emotional as far as matters pertaining to bhallaldeva. So why this love didn’t extend to his grandson?

Safe to assume, bhadra is adopted. Which leads to the reason that had bhallaldeva married someone, he’d definitely have had an heir of his own, considering his narcissistic and egoistic attitude.