Seems kind of pointless on a Dragonfire Adept. Just saying. It’s much better than Half-dragon, but Dragonfire Adepts get most of the benefits of Draconic anyway by virtue of their class features. Yes, you don’t have the natural weapons, but your dragon breath is better much of the time anyway. The dragonfire adept does not have good melee skills.
No, it’s much superior to Spring Attack, because you get a normal Standard Action rather than just getting to make an attack. Since Spring Attack is a full-round action, you cannot combine it with Fly-by Attack. Spring Attack is a really awful feat anyway.
Hover and Wingover
Hover is basically required for anyone who has less than Good maneuverability and needs to make Full-round Actions (most importantly Full-Attack). As a dragonfire adept, your draconic flight invocation gives Good maneuverability, and you don’t really need full-round actions much anyway. Pass.
Wingover isn’t nearly as useful in general, but again, your Good maneuverability means you don’t need it at all. You can reverse by default and lose only 5 feet of moevement, unlike Wingover which costs 10.
Feats for Natural Weapons
I really don’t recommend focusing too much on your natural weapons unless you plan on multiclassing or prestige classing for some better BAB and HD, or for better natural weapons than Draconic gives you (Totemist from Magic of Incarnum and Psychic Warrior from Expanded Psionics Handbook are the two reigning champions of the natural-weapon schtick, for reference).
Anyway, Multiattack is probably a decent pick-up for you, particularly if you’re required to treat the claws as secondary, but I probably wouldn’t bother with Improved Multiattack. Going from −5 to −2 is a pretty big deal; going from −2 to −0 is less so. Sure, go for it if you have extra feats, but who has those? Normally Multiattack is must-have for a natural-weapon attacker, but you only have three so it’s less crucial.
In addition to that, Improved Natural Attack is not an awful feat by any means, but you’d only get to apply it to either Bite or Claws (or take it twice for both), which is kind of lame.
And if you can manage to get one of the required types (aberration, dragon, elemental, magical beast, or plant), Rapidstrike and Improved Rapidstrike from Draconomicon are excellent at higher levels.
Finally, at low levels, you’ll have a lot more attacks than anyone else, so dipping Rogue or another Sneak Attacker and taking Craven (Champions of Ruin) could be very useful.
Items for Natural Weapons
Consider picking up a necklace of natural attacks from Savage Species, or failing that, an amulet of mighty fists (with three natural attacks, the amulet of mighty fists is no longer strictly overpriced, though I’d argue it still is).
Dragon Magic’s fanged ring is also solid, but notice that the wyrmfang amulet from the same book was reprinted in Magic Item Compendium for less money. Also in MIC, a combination of the bracers of the arcane and the ring of adamantine touch allow you to handle some DR that would otherwise be problematic. Along the same lines, ghost shroud (still MIC) grants Ghost Touch, which will help you out with incorporeals.
Bonus: Feats for Breath Weapons
Mostly, I want to mention Entangling Exhalation from Races of the Dragon. This feat turns your breath weapon from fairly-meh damage to fairly-meh damage plus half-decent crowd control. The combination turns the breath weapon from an OK-ish option to a great one. There are other [Breath] feats in Races of the Dragon that are worth considering, though none are as good.
In Draconomicon, we instead have [Metabreath] feats, which are different because they require a breath weapon that has a “cooldown” period. Many argue that the dragonfire adept’s doesn’t qualify. However, if your DM lets you qualify, or you get another breath weapon that does have a cooldown (the Dragonborn of Bahamut template is a pretty easy option, for example), you can apply the feats to your dragonfire adept breath weapon. Entangling Exhalation’s still better but they do give you some more options.