Here's how this could work, step-by-most-restrictive-step
Combat is in progress. Bob and Gack are adjacent to each other. For convenience, this answer assumes Bob ignores the usual 25% arcane spell failure chance of the typical breastplate by preparing and casting his spells using the extraordinary ability rune magic of the Races of Stone prestige class runesmith (118–20). I mean, really, that's probably why Bob took the class.
On Bob's turn, Bob takes a swift action to cast the 1st-level Sor/Wiz spell blades of fire [conj] (Spell Compendium 31) so that the spell affects one of Bob's gauntlets and Bob's armor spikes. The spell's description, in part, says, Bob's affected "melee weapons each deal an extra 1d8 points of fire damage."
Bob takes a standard action to cast on the defensive—by succeeding on a Concentration skill check (DC 16)—the 1st-level Sor/Wiz spell corrosive grasp [conj] (SpC 53). That spell's description says
A touch attack with this hand causes 1d8 points of acid damage. You can use this melee touch attack up to one time per level. You can also deal this damage as extra damage with an unarmed strike or an attack with a natural weapon. If you grapple an opponent, you can deal this damage in addition to other damage you deal with a successful grapple check.
At your table, the special attack grapple can be used on the same turn that a creature casts a touch spell, but while making an armed touch attack with a spell effect usually doesn't provoke an attack of opportunity, making a grapple attempt still does! Thus Bob, as part of the standard action to cast the spell corrosive grasp, makes the special attack grapple against Gack. This provokes an attack of opportunity from Gack that Gack makes and with which Gack misses. (Had Gack hit Bob, Bob's grapple attempt would've been foiled, making this a risky strategy for Bob!)
Bob makes the touch attack to start the grapple and succeeds, hitting Gack with one of the 5 charges from Bob's corrosive grasp spell and dealing Gack 1d8 points of acid damage. His touch attack successful, Bob takes a free action to try to get a hold, Bob making an opposed grapple check against Gack. Bob wins, causing Bob to deal Gack Bob's unarmed strike damage (typically 1d3 points of nonlethal bludgeoning damage plus Bob's Strength modifier). Bob moves into Gack's space to maintain the grapple. Bob's turn ends.
By this really strict reading, Bob's dealt Gack 1d8 points of acid damage and 1d3 + Bob's Strength modifier nonlethal bludgeoning damage.
"Wait! Wait! What about…?"
First, the Player's Handbook isn't entirely clear on how spiked armor/armor spikes work in a grapple. The description of armor spikes says, "You can have spikes added to your armor, which allow you to deal extra piercing damage… on a successful grapple attack" (124), but that's the extent of the explanation of how that works. Dealing damage isn't mentioned in conjunction with other uses the term grapple attack like in the PH here, the DMG here, and the MM here.
So if the DM rules that the extra damage from armor spikes applies, for instance, whenever a creature so equipped succeeds on an opposed grapple check that deals damage—including when a creature during the special attack grapple's Step 3: Hold deals its unarmed strike damage—Bob would also deal Gack the armor spikes' extra +1d6 points of piercing damage and the blades of fire spell's extra +1d8 points of fire damage.
(As the armor spikes' description has the spikes dealing extra damage, this reader thinks that a creature benefiting from armor spikes in this fashion does not add its Strength modifier to the armor spikes' damage, in the same way that a rogue doesn't add her Strength modifier to the extra damage granted by the extraordinary ability sneak attack. Of course, the DM may rule otherwise, but this reader considers that possibility remote enough that this additional iteration of the armor spikes' wielder's Strength modifier is excluded from the damage summary at this section's end.)
Note that an unsourced Main FAQ entry—and of all the FAQ entries, that kind is this reader's least favorite—takes a stab at clarifying how to use armor spikes. In part, that FAQ entry says
When grappling, you can damage your foe with your spikes by making a regular grapple check (opposed by your foe’s check). If you succeed, you deal piercing damage to your foe (see Table 7–5 in the PH) rather than the unarmed strike damage you’d normally deal when damaging your foe with a grapple check. Since you can use armor spikes as a light weapon, you can [also or instead] simply use them to attack your foe. You suffer a −4 penalty on your attack roll when attacking with a light weapon in a grapple…. (53)
Keep in mind that this Main FAQ entry seems to ignore—or, at least, read differently from the game's normal use of it—the word extra in the armor spikes description. Nonetheless, if the DM uses this Main FAQ ruling then the armor spikes (and the blades of fire spell that targeted the armor spikes) are inconsequential for Bob on the turn during which he established the grapple.
Second, the spell corrosive grasp says that the caster "can deal [the spell's] damage in addition to other damage you deal with a successful grapple check," but whether this means any ol' successful grapple check that happens to deal damage—like the one that Bob made to get the hold—is up to the DM. That is, one alternative reading would, for example, see the DM rule that the damage from the corrosive grasp spell applies only when the caster successfully takes the grapple option Damage Your Opponent. It's possible, though, that here the DM will rule that Bob discharges a second charge from the corrosive grasp spell effect and deals Gack, in addition to other damage, another 1d8 points of acid damage.
Third, that gauntlet? The one that Bob also targeted with the blades of fire spell? That's probably no help in dealing more damage at this point. The description of the gauntlet, in part, says, "This metal glove protects your hands and lets you deal lethal damage rather than nonlethal damage with unarmed strikes. A strike with a gauntlet is otherwise considered an unarmed attack" (PH 117–18 and emphasis mine). When Bob makes the touch attack to deliver the touch spell effect that also starts the grapple, Bob isn't making an unarmed strike and isn't striking with the gauntlet.
(To be clear, Bob's just making a touch attack against Gack not an unarmed strike, this despite Bob being technically unarmed when he makes the touch attack with the spell effect. Bob's also not smacking Gack upside the head with his gauntleted fist, which is what this reader boldly assumes is a strike with a gauntlet. The spell blades of fire needs a melee weapon to deal damage so that the spell's effect can deal extra damage, and the gauntlet here isn't dealing damage.)
Further, while establishing a hold deals Bob's unarmed strike damage, Bob's not actually making an unarmed strike then, either. Of course, the DM could rule otherwise—I mean, the words unarmed strike are really in Step 3: Hold, after all—, but this player wouldn't count on such a ruling. Nonetheless, with the right DM, if you brought beer, Bob could here see his blades-of-fire-spell-affected gauntlet deal Gack another 1d8 points of fire damage.
Fourth—and I am extremely hesitant to mention the rule because it should never be used, but I don't know how deep folks at your table dive for opportunities to deal more damage, and I suspect comments would bring it up even if I didn't—, there's the terrible rule about unintentional discharges. (Go ahead. Make jokes. Please. The rule is one anyway.) That rule says, "If you touch anything or anyone while holding a charge, even unintentionally, the spell discharges" (PH 141). (Yes, that's all of it in its entirety. Don't use it.) How and if the DM employs this rule in this situation an utter mystery, but at some point the DM may rule Bob expends a third charge from the corrosive grasp spell, dealing Gack another 1d8 points of acid damage, but, honestly, there's no hangin' way I can know at what point that'd happen. So I'm clear, this rule is only mentioned for completeness; I recommend the DM not use this rule at all.
In other words, if everything's coming up Bob, Bob could deal Gack 3d8 points of acid damage, 2d8 points of fire damage, and 1d3 plus Bob's Strength modifier points of nonlethal bludgeoning damage—or, instead, lethal damage if the DM rules the gauntlets apply—and an extra 1d6 points of piercing damage.
Note: This DM has the melee touch attack that a caster can make on the same turn as casting a touch spell only be regular, everyday melee touch attack rather than allowing that melee touch attack to substitute for the touch attack that's necessary to make the special attack grapple. Thus I have done my best to create a walkthrough of a process that I urge you to have explained to you step-by-step instead by your DM.