It's likely that the portrait is simply not a major plot point and its fate is left ambiguous.
However, there is a popular misconception that the portrait is destroyed in the fire at Tara at the end of the book. This idea likely stems from the iconic scene in the movie where the portrait is shown hanging in the Tara parlor, and it's easy to assume it's destroyed alongside everything else.
But there is no evidence in the book to support this. It's worth noting that Margaret Mitchell, the author, was known for her meticulous attention to detail, so it's highly unlikely that she would have omitted such a significant detail if it was intended to be destroyed.
Ultimately, the fate of the portrait is left to the reader's imagination.