Note that due (presumably) to a coding error, the flexible award search URL is not superfluous; it currently provides a function unavailable through the regular Award booking URL. On the regular Award booking page (even if you go there the slow way, i.e., via the Advanced Search link), clicking the One Way radio button disables the Flexible Search check box. If you cleverly click the FS check box before clicking One Way, the FS option is ignored. When you use the Award Flexible Search URL then click One Way, the FS option is still disabled on the form, but works correctly when the form is submitted.

To break the tie for clues as to what was intended, we can look to the modal search form on the award list page. On that form, the FS box remains enabled for both RT and OW searches (note the subtle color difference between it and the adult pax box):