Perhaps this might have happened had the British made an even greater show of force at the Battle of Jahra than just some airplanes and three warships, or if you had a British Political Resident in the Persian Gulf less friendly to Ibn Saud than Percy Cox. Even after OTL's giving up 2/3s of Kuwait's territory, the Saudis still blockaded Kuwait until 1937, so this TL could hardly be much worse unless the Saudis resume the war, breaking the treaty, and bring the British down on them later in the 1920s and convince them on finally giving up on trying to annex Kuwait. This would also mean there would be less anti-British sentiment in Kuwait in the 1930s.
Kuwait's economy will still crash as the Depression hits with the loss of international trade and Japan's invention of cultured pearls devastating their pearl industry. When oil gets discovered in the 1930s - earlier, maybe if Kuwait builds that commercial city in the south that they had wanted to in 1919 before the British dissuaded the Kuwaiti Sheikh in a futile attempt to prevent the future conflict between Ibn Saud and Kuwait - Kuwait will regain importance, and there probably won't be a 'Free Kuwaiti Movement' to unite Kuwait with Iraq. Post-WW2, Kuwait begins its public works projects. In the early 1950s they were already the largest oil exporter in the Persian Gulf, in TTL they're even bigger. Without the initial 'Free Kuwaiti Movement' and its quashing by the Al Sabahs with British support, Iraq may feel they have less casus belli against Kuwait. Nevertheless, Iraq is still going to want Kuwait and whatever crisis eventually emerges may cause Kuwait to arm even more than OTL with even more oil revenues and a larger population to draw upon, to the extent that Iraq isn't going to be able to launch a surprise attack that swiftly occupies the country as happened in 1990 in OTL. There will either be a noticeable military buildup of Iraqi military forces nearby, or a surprise attack will get bogged down fighting a larger Kuwaiti military long enough for international aid to get involved before a full occupation.