In William Golding's Lord Of The Flies, why do the boys need face paint in order 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.