Though it's currently unclear whether or not the White Flame in "The Witcher" is hunting down Ciri for the same monstrous reasons as his book counterpart, it's worth noting that there are plenty of other groups who are after Ciri and her rare elder blood.
In Season 3 alone, there are at least three other groups searching for Ciri alongside the White Flame, each of them hoping to use her elder blood in a unique way to gain power. Most prominent of these hunters is the Redanian Chancellor and spy Dijkstra (Graham McTavish), who seeks to capture Ciri and marry her to King Vizimir of Redania (Ed Birch ) — thereby uniting Redania and Cintra under one ruler. Another conspirator hunting down Ciri is the elven ruler Francesca Findabair (Mecia Simson), who wants Ciri because she believes that her elder blood will usher in a new age of elven prosperity and power.
Finally, Ciri is consistently being tracked by an otherworldly group of Aen Elle elves known as The Wild Hunt; inhabitants of another realm who believe that they can use Ciri's powers to wreak chaos across multiple different worlds. Although the White Flame might have the most twisted plans in mind for his daughter, it's clear that Ciri's elder blood has made her a prime target for the Continent's most important figures.