Capture one to export a progressive jpeg?

Capture One does not appear to have the ability to export to progressive JPEG directly. The programmers have done the "right thing" by not giving users the option to easily create progressive JPGs.

Although progressive JPGs are slightly smaller (about 1%), they are significantly slower to create and display. Modern browsers, viewers, and editors also do not display progressive JPGs progressively. So there is little benefit to using progressive JPEG at all.

While you could export to an intermediate format, which you later convert to progressive JPEG, most image formats are compressed, so exporting to an image then converting to JPG would in most cases result in compressing the image at least twice. While you may not lose any image data, the process does waste time in return for little benefit. This is especially true for PNG, which can be very slow to save.

TIFF images can be saved uncompressed, but the files are very large, so it can still take a significant amount of time to save, even though the compression step is skipped.

Unless you have a very good reason to use progressive JPEG, you should just export directly to JPEG from Capture One.