Yes, there is a chance.
However, it is still not very high. It will be a lot better if the other parent also has 6 (or at least, several) perfect IV's. This is because the Destiny Knot takes IV stats from both parents. This means that it might take the Attack stat from the Ditto, but the Speed could come from the other parent. It is just luck as to which the IV's will come from.
As for being Shiny, it will just be the same as normally doing the Masuda Method (chance of 1/1365)
And for being both Shiny and having IV's, well it is certainly possible, but the chance is rather small, unless both parents have 6 perfect IV's, in which case the offfspring is pretty much guaranteed to have 5 or 6 perfect IV's, and so the chance is the same that of getting a Shiny.
Sources: Destiny Knot and Masuda Method