In Complete Arcane a Warlock's Eldritch Blast increases with warlock levels.
The Dragonfire Adept, from Dragon Magic, is a similar class with a breath weapon and invocations has a descriptor that specifically states it gains invocations, caster level, and breath weapon dice and DC with any class that increases "effective spell casting class levels".
The Edlritch Disciple in Complete Mage specifically states each level increases known invocations and caster levels "as if you had gained a level in an invocation-using class to which you belonged..." followed by a parenthesis (this includes Eldritch Blast).
The Hellfire Warlock states "plus 2d6 points of damage per class level".
Warlock levels vs class levels terminology. I see a bigger problem here to be honest...do "effective spellcasting levels" of Hellfire warlock even increase invocations? For the sake of arguement:
Lets say I took levels of Wizard, then Red Wizard, and then say, Eldritch Knight, but I targeted Red Wizard with it's progression. Can it work that way or must I target the class that originally gives spellcasting? If you take a solid look, Hellfire Warlocks technically DON'T learn invocations on their own, meaning you could argue that an Eldritch Disciple can't even advance Hellfire Warlock since it merely advances existing Invocation use, and does not provide it.
Let's say your DM ruled it IS an invocation class you can advance with a PrC, does it's progression then forward to the original class? If not then sure you're increasing hellfire damage, but not Invocations or Eldritch Blast dice/level/DC.
HOWEVER. There's been a post somewhere (I'm going to look for it later) that a player asked a Dev about Practiced Spellcaster being applied to Eldritch blast. The Dev replied that he would rule for it, seeing Eldritch Blast as something that refrences it's owners caster level. He admitted that the exact wording wouldn't support it, but the spirit of the feat is there. This would be supported by the advancement of Eldritch Disciple and Dragonfire Adept.
In this case, Warlock's Eldritch blast references caster level, not class level. At this point your DM would have to make the call. I would have to say it's referencing the "class level" of the Hellfire Warlock alone and not the Hellfire Warlock's "caster level" which is far greater due to previous Warlock levels, making both the PrC and the feat unable to apply to Hellfire Blasts.
If your DM decides to allow PrCs to be true proxy's for the classes they advance, then I would rule yes. If they say it must be the class that originally provided the use of Invocations, then there's no way to increase Hellfire Blasts beyond 6d6.