Here's a link to the Triumph racing parts catalog for the Daytona 675. The slipper clutch is on page 23 and yes it will work with the Street Triple.
http://triumph.co.uk/media/DaytonaRa...ualIssue_2.pdf
With that said I can't see a need for it on the Street it has very little engine braking and a very smooth on off throttle transition. If you are going to be doing a lot of track time I could maybe see getting it but you would be better off with a Daytona in that case anyway. Something that is rarely mentioned when people talk about slipper clutches is clutch plate life. Depending on how you ride I've heard of clutch plates in a slipper clutch wearing out anywhere from 1,000miles to 10,000miles.