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At stumps, New Zealand was 145-2 in reply to the West Indies' 307 at McLean Park, giving the hosts the upper hand in the slow-moving match affected late on Saturday by a short rain delay.
Flynn was out for 57 close to stumps, his second half century in tests after his breakthrough innings of 95 in the drawn first test.
The left-handed opener McIntosh, a painstaking batsmen finding his feet in the test arena, had reached his highest test score of 62 not out. He will resume tomorrow with Ross Taylor (4 not out).
West Indies paceman Fidel Edwards claimed both wickets to have 2-26 by stumps. Flynn and McIntosh re-established the innings after the loss of opener Jamie How for 12 when the total was 19. Confronted by tight bowling -- a West Indies attack determined to exert pressure through containment -- the pair took 30.2 overs to raise New Zealand's 50 and 98 minutes to post their 50 partnership.
Flynn reached his half century in 134 minutes with four boundaries and two sixes and McIntosh had batted more than four and a half hours for his 62 runs by stumps.
He owed his continued presence at the crease to an almost comical mix up between Edwards and wicketkeeper Denesh Ramdin when he was 14 and New Zealand was 36.
Attempting to pull a bouncer from Edwards, McIntosh succeeded only in hitting the ball straight up in the air but as wicketkeeper and bowler converged. Both called but neither attempted the catch.
Earlier, Iain O'Brien claimed the last four West Indies wickets to finish with a career-best 6-75. Shivnarine Chanderpaul, who resumed on 100, finished unbeaten on 126 after batting for five hours and 40 minutes. The not out innings was enough to lift his career average above 50, and extended his remarkable record over the past 18 months in which he has averaged 103 in tests.
Remarkably, his innings in Napier was his highest score and first century against New Zealand in tests, surpassing his 82 at Bridgetown in 1996.
He has become so hard to remove since the England series last year that the average duration of his completed innings in that 18-month period has been 6 1/2 hours.