Your Pokemon will still eventually breed, though breeding two Pokemon with Different OT numbers does increase the chance of getting an egg. This chance is increased even more if they are same species. So you could try breed two Delphox from two different games, that's the most effective method of trying to get an egg in the daycare.
Of course, you can still breed with Ditto as I'd imagine it'd be hard to get another Delphox, but at least try get a Ditto (or any Pokemon in the Field Egg group for that matter, assuring it's a female) that has a different OT number to your Delphox. The above seems like the most effective way of getting an egg.
Getting a female Fennekin is a one in eight chance, so it shouldn't be too hard unless you're really impatient like I am (xD), however getting a shiny is much more harder. I'd recommend using the Masuda Method, which breeds two Pokemon that are compatible, but also are from different regions. (Like a Japanese Ditto and your supposed English Delphox) This increases the chances significantly, and it's a very effective way of getting a shiny Fennekin through breeding.
Hope I helped. :)
Sources: Experience and Source