The design flaws are that battle damage can lead to the ship filling with avgas fumes due to damage to storage and transfer arrangements. That's pretty much what happened to Ben-my-Chree, and the RN subsequently became as paranoid about avoid a repeat of it as they were about flash protection to capital ship magazines as a result of Jutland. As Athelstane pointed out, Lexington didn't blow up because her crew failed to do their jobs as they'd been trained to, but because their ship's design flaws made her insufficently resilient to shock damage, and she therefore leaked fumes all over the place and turned into a fuel-air bomb. The USN had never had an aircraft carrier (in the widest sense of the term) come under serious attack, so they didn't have experience of the sort of problems that could be caused. The ideal solution would have been to stop construction on all carriers and resign them to RN avgas handling standards, but there was a minor issue to deal with called the IJN that precluded that, so Lexington's crew came up with a less-than-ideal but still pretty effective stopgap.
Disclaimer, I am not an expert or well-read on the design specifics of USN or RN aircraft carriers, but to suggest that American carriers were more fragile because of design flaws (and specifically what about the avgas storage methods and piping made them susceptible to battle damage and what did the RN do to correct the "flaw") is not born out by combat records of any class of American carrier; CVEs excluded. At Coral Sea,
Yorktown had a SAP bomb penetrated her flight deck and damage an avgas room, as well as boilers. She also suffered damage to her hull integrity due to almost a dozen near misses. She suffered neither a catastrophic explosion like
Lexington nor was she sunk due to cumulative damage. At Midway, she suffered multiple bomb hits, including hits on her boilers, ammunition, and fuel storage, but improved DC practices prevented major fires from spreading. Even after a second successful attack, one which occurred I might add because the American damage control was so good the Japanese thought she was an unscathed carrier, she was still afloat and not sinking until I-168 sunk her.
An awesome counterpoint to your assertion that USN avgas storage and fueling systems were flawed, is the USS
Franklin which was bombed in the middle of fueling and arming a strike, detonating 13 to 16 tons of high explosive, as well as aircraft in the hangar deck which were fueled and armed, causing an avgas explosion. Despite this damage, similar damage of which killed all four Japanese carriers at Midway,
Franklin survived her damage and evacuated the battle area under her own power.
British carriers were hardier than their American counterparts, they were expected to operate in the North Sea and the Mediterranean where they would be at high risk of attack by larger numbers of more capable land-based aircraft. They paid for this with air groups that were barely, or less than, half the size of an American carrier and were noted as being cramped and awkward to operate in with tight hangars and because of a refusal to practice deck park or conducting turnaround operations on the flight deck, significantly reduced sortie rates due to the closed hangar; you can't warm up warplanes in a closed hangar for the same reason you don't start your car with the garage door closed.