Chicago teachers voted overwhelmingly to go on strike, approving the third walkout in as many years against the nation’s third-largest school system. Of 28,000 rank-and-file union members, the teachers voted 3,548 to 494 to reject the latest wage increase offered by the school board and then returned to negotiations, almost certainly delaying the scheduled start of school today. A last-minute appeal by Gov. James R. Thompson failed to bring the Chicago Teachers Union and Board of Education into agreement. Teacher walkouts have already idled nearly 46,000 students in Illinois and Michigan.