The Dahon Curl folds in the same shape and just a bit smaller than the Brompton*. Any travel case that will work for the Brompton will work for the Curl. There are numerous web pages discussing a myriad of nuance on the subject of travel on airlines with the Brompton.
I use a Samsonite Stryde Glider Long Journey hard-sided suitcase to fly with my Curl. The folded bike drops right in with no disassembly. You'll want to pad around it. The commercial Samsonite suitcase 1) has a less expensive street price than the hard-sided Brompton-specific flight cases 2) is lighter than other hard-sided Brompton-specific flight cases, which gives you more 'headroom' under the max bag weight limit of the airlines.
*I've had the two bikes folded side-by-side. I've had Brompton owners dispute this information - even after I posted pictures of the Brompton sticking up above the Curl.