They were outclassed in the first set as Ukraine’s Kichenok and New Zealand’s Routliffe, who have won three Grand Slam doubles titles between them, raced to a 4-1 lead before taking the set with another break three games later.
Raducanu and Boulter came from 4-1 down to level at 4-4 in the second set.
Their best chance to turn the match around came in the following game, but they failed to convert four break points.
Despite saving three match points three games later, they succumbed to defeat.
Raducanu faces Rebecca Sramkova in the last 16 of the singles on Thursday and Boulter takes on fifth seed Diana Shnaider.
Raducanu can replace Boulter as British number one if she equals Boulter’s results at Queen’s, which is hosting a women’s tournament for the first time in 52 years.
Boulter has held the position for two years since she took over when 2021 US Open champion Raducanu slipped down the rankings following injury and inconsistent form.