Lord of the Flies definitely exhibits some aspects of fascism, especially as Jack gains power over the boys and makes himself chief. Jack's push for total control reflects the fascist ideology, in the way that fascist governments try to achieve total control over the state and the individual. As leader, Jack establishes himself as an all-powerful dictator over the other boys and uses fear and intimidation to maintain his power, much like Mussolini and Hiter did over Italy and Germany.
When faced with opposition, Jack seeks to eliminate his opponents quickly, and multiple examples within the novel support this conclusion such as Piggy, Samneric, and Ralph. Moreover, Jack also uses the hunting dance as a unifying anthem for the other boys, drawing them to his power in excitement or fervor, much like Hitler and Mussolini used rallies and speeches to cultivate the masses' support.
One last fascist element in Lord of the Flies is how Jack seeks to control the means of production on the island, similar to how fascist governments sought control of factories and production; Jack's seizure of Piggy's glasses and the means to make fire strips his opponents of the ability to produce any fire themselves or to cook food.