Did king George the III own slaves?

No.

At the time, Britain had outlawed slavery. But as for King George's view on it, he did not support the anti-slavery cause.

... Actually, he did support the Anti-Slave cause. King George The Third participated in the Sugar Boycott and spoke of his personal dislike of slavery, and one can read of this in his Biography by John Brooke.

He was also the King who signed into Law the abolition of the slave trade in 1807.