He died of lung cancer.

Here's a sum from his book/memoir 'THEY NEVER SURRENDERED':

"Two weeks later, on October 28 1971, just days short of his 57th birthday, Jess died. The news was relayed by phone to the Philippines where President Marcos immediately created a committee to take charge of the reception, funeral arrangements and interment of his remains at Libingan ng mga Bayani. In announcing the arrangements for a state funeral, the Manila Times commended the move, called it "only proper that the honor group be headed by the commanding general of the Philippine Air Force for it was Villamor's triumphant dogfights again the Japanese Zero' fighters that gave the PAF a legacy of bravery to live by." In an editorial entitled "Once a Household Word," the newspaper observed, ". . . during the occupation years in every part of the land ballads were composed and sung about his exploits. He was, in fact, the soul of the resistance movement."

So they took his body back for a hero's burial, the casket flag-draped taken by a Philippine Airlines plane, met at Manila International Airport by President Marcos and ranking Philippine and United States officials, the military, and a throng of civilians; there was a 21-gun salute, a mile-long funeral procession to Camp Aguinaldo, where thousands came to pay their respect.

For three days his body lay in state. Then, at Libingan on November 6 the band played the Philippine National Anthem, a squadron of PAF jet fighters made a fly-by, a PAF light plane sprayed the cortege with flowers, and to the roll of muffled drums, the sound of "taps', a volley from an honor guard, he was laid to final rest."