In Lord Of The Flies, why do the boys need face paint to do evil deeds?

The face paint is a camouflage to hide their true identities. Once their faces are covered, they adopt new personalities. They are transformed from innocent and disciplined English schoolboys into savage hunters. The paint symbolises their descent into savagery and bloodthirst.

The boys had obviously learnt about war paint and the use of paint for camouflage at school or through their reading. They had most probably also come into contact with soldiers, during their evacuation, wearing camouflage uniforms and probably face paint since their country was involved in a war. It is, therefore, natural for them to adopt a similar strategy when they go on a hunt. The face paint would allow them to blend in with their surroundings and become less noticeable to their prey, as Jack explains to Roger whilst smearing his face with clay in chapter 4:

“For hunting. Like in the war. You know—dazzle paint. Like things trying to look like something else—” He twisted in the urgency of telling. “—like moths on a tree trunk.”

In addition, since they are young, it is also fun. The putting on of a mask allows them to do some role-play. They can now experience greater freedom and adopt the persona of whatever or whomever they wish. The mask makes them different, as illustrated in the following extract relating to Jack after he disguised himself:

He looked in astonishment, no longer at himself but at an awesome stranger. He spilt the water and leapt to his feet, laughing excitedly. Beside the pool his sinewy body held up a mask that drew their eyes and appalled them. He began to dance and his laughter became a bloodthirsty snarling.

The psychological impact of their hidden selves encourages them and makes them behave in contrast to what they have become accustomed to. They do not have to subscribe to society's conventions.  

Ironically, though, the masks also bring the boys closer to their real natures. They are now more in touch with their innate desire to harm and hurt and maim. They feel released from the pretence of civility and conscientiousness. They have, now, after all, been reborn as savages. Wearing the face paint is accompanied by whooping and yelling and chanting and doing dances and hunting and killing because these are the things savages are supposed to do. 

Jack and his hunters become tribal and refer to themselves as savages, which means that they exist as a separate entity. Their savagery is an element of their nature since they are, after all, supposed to be wild and free because that is what being savage means. Painting their faces further confirms this fact - we are not what we are supposed to be, we are what we are: what you see is what you get. 

Simon recognises this beast which exists within us all and he, Ralph and Piggy, the more rational ones, become victims of the other boys' descent into barbarity. In the end, Simon and Piggy are killed and Ralph is hunted like a beast. 

How does face paint change the boys beyond camouflage in Lord of the Flies?

Lord of the Flies, by William Golding, is a particularly symbolic novel, and the face-painting which Jack and the other hunters do is certainly more significant than just serving as simple camouflage they use to hunt pigs.

Jack is the first boy to paint his face (chapter 4), and he does so initially because he thinks the pigs are seeing him rather than smelling him, which keeps his hunts from being successful. It is a rather startling sight for the other hunters, at first, to see the red, white, and black paint all over Jack's face; however, Jack is mesmerized as he looks at his painted-face reflection in the water. 

He looked in astonishment, no longer at himself but at an awesome stranger. He spilt the water and leapt to his feet, laughing excitedly. Beside the pool his sinewy body held up a mask that drew [the others'] eyes and appalled them. He began to dance and his laughter became a bloodthirsty snarling. He capered toward Bill, and the mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness. 

Throughout the rest of the novel, Jack's painted face is almost always referred to as a mask; and, as this quote indicates, this mask  serves to insulate him from "shame and self-consciousness." The result is a "bloodthirsty snarling" hunter who has become a killer and does not care who or what he kills, for once these restraints of civilization are removed, anything becomes acceptable. Soon the rest of Jack's "tribe" will wear the paint and become Jack's followers in crime, and nearly all civilized behavior is lost. 

What do the changes in Jack's face paint symbolize in Lord of the Flies?

In chapter 4, “Painted Faces and Long Hair,” Jack paints his face for the first time. He had the idea to provide camouflage when they hunt the pig in the forest. Jack calls camouflage “dazzle paint.” He finds white and red clay, which he digs up and stores in two leaves. The boys also use charcoal from the fire to make black. As he smears the clay onto his face, he wishes he had green clay as well. As Roger watches, he does not initially understand what Jack is doing. Jack explains that this homemade version of dazzle paint is “for hunting,” like people do in a war.

Looking at his reflection in the water, Jack does not like his first effort. He rubs it off and systematically applies the clay and charcoal.

He made one cheek and one eye-socket white, then he rubbed red over the other half of his face and slashed a black bar of charcoal across from right ear to left jaw.

In his new reflected image, Jack sees “an awesome stranger,” and it inspires him to dance around and snarl at the others.

In chapter 8, following Jack’s success in leading the hunt and killing the pig, he is emboldened to challenge Ralph’s authority. After almost all the boys defect, he organizes a feast and storms into the camp to confront Ralph and Piggy. Although the hunt has long ended, his face is still painted, but he wears no clothes.

Stark naked save for paint and a belt, was Jack. ... He was safe from shame or self-consciousness behind the mask of his paint.

Later, when Ralph and Piggy decide to attend the feast Jack invited them to at the new camp, they find Jack painted again. On a huge log, “Jack, painted and garlanded, sat there like an idol.” He urges the boys to accept him as their chief, and the narrator no longer refers to his face but calls it a mask.

Jack … turned his mask down to the seated boys and pointed at them with the spear.

“Who's going to join my tribe?”

When they remain silent, he exhorts them into a frenzied dance, during which they kill the “beast,” who is really Simon.