The area where Delphox really shines is its Speed and Special Attack. It doesn't have a very good movepool, though, so most opponents will be able to predict what you're going to do. I noticed that Delphox gets Future Sight, and while the move isn't used that often I think Delphox has the potential to pull it off.
Delphox w/ Leftovers/Life Orb
252 Special Attack/ 252 Speed/ 4 HP
~HP Fighting/Calm Mind
The goal here is to scare your opponents into switching into something that resists Future Sight, and then hitting it with Grass Knot or a STAB fire move. Send Delphox in on something like Forretress and use Substitute. When Forretress switches, use Future Sight. If you're running Calm Mind, use that before your Sub is destroyed. I would rather run HP Fighting, however, because the chances of Tyranitar being sent in to counter Delphox is pretty high. If you're running Fighting, use whichever move will deal the most damage before your Sub gets destroyed. Now your opponent has two options: Keep their Pokemon in, which hopefully took a big hit from your Delphox, and get KO'd by Future Sight, or switch and let something that resists Future Sight switch in. Depending on what they have on their team, use Flamethrower/Fire Blast (less power or more reliability), or Fighting/Calm Mind again, depending on which one you're running. Calm Mind will possibly give you some big boosts, while Fighting gives more coverage. As for items, Leftovers or Life Orb work equally well here. I personally would use Leftovers to give myself more staying power, to possibly run another Substitute if I had the opportunity, but Life Orb gives more power, plus it's unlikely that your Delphox will stay in the game long anyways. If you're running Calm Mind almost definitely use Leftovers, since you won't get much sweeping opportunity with your low Defenses. Partners for this set would be anything that benefits from a potential wall being severely weakened. Gimmicky sweepers like Scolipede would love to have the likes of Tyranitar and Gliscor KO'd or weakened.
Delphox also has pretty good Speed, and can make a decent Choice Specs sweeper.
Delphox w/ Choice Specs
4 HP/252 Special Attack/252 Speed
The goal of this set is simple. Use Psyshock to deal with annoying Pokemon like Chansey or Blissey that would otherwise wall Delphox. Flamethrower gives more accuracy while Fire Blast gives far more power. Shadow Ball rounds out the coverage, allowing you to hit Jellicent and Reunicleus hard. Solarbeam and Grass Knot depends on whether you're using Mega Charizard Y and/or Ninetails for Sun. Use Solarbeam if you've got Drought, but otherwise use Grass Knot. Partners for this set would be Ninetails/Mega Charizard Y, something to give you a powerful Solarbeam, a Pokemon with decent priority to clean up Mega Alakazam/Mega Gengar, like Talonflame, and walls that can resist things that would otherwise ruin Delphox's day. Avalugg, Chensaught, and Skarmory all provide good defense and resist/can withstand most of the attacks that would be directed at Delphox, like Aqua Jet, Earthquake, and ExtremeSpeed.
All in all I don't think Delphox will see much usage in standard play, but due to its typing and possible coverage, it shouldn't be ruled out. Base 104 Speed and base 114 Special Attack are stats that shouldn't be overlooked.