You need to convert the subtitles into some sort of either text or graphic format.
As text, you might be able to create text generators in Final Cut, and superimpose in the usual way, or depending on the HTML, convert that in a captioning/subtitling application like MacCaption and import either a QT movie or FCP XML onto a timeline and proceed as per usual.
Or export a lot of graphic files -- png or tiff or whatever works for you and composite those onto a timeline. Otherwise it is not likely there is a Quicktime Pro or DVD authoring-type of procedure that will magically produce a subtitle track.
"I always pass on free advice -- its never of any use to me" Oscar Wilde.