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You can deliver a touch spell like Touch of Combustion using a claw attack, but it takes a new standard action to make the attack roll instead of being a "free" touch with the casting of the spell.
If you don’t discharge the spell in the round when you cast the spell, you can hold the charge indefinitely. You can continue to make touch attacks round after round. If you touch anything or anyone while holding a charge, even unintentionally, the spell discharges. If you cast another spell, the touch spell dissipates. You can touch one friend as a standard action or up to six friends as a full-round action. Alternatively, you may make a normal unarmed attack (or an attack with a natural weapon) while holding a charge. In this case, you aren’t considered armed and you provoke attacks of opportunity as normal for the attack. If your unarmed attack or natural weapon attack normally doesn’t provoke attacks of opportunity, neither does this attack. If the attack hits, you deal normal damage for your unarmed attack or natural weapon and the spell discharges. If the attack misses, you are still holding the charge.
If you successfully hit then the claw would deal damage and also discharge the spell. The charge from the spell would also deal damage (assuming it overcame any SR). So both the claw and the spell would deal damage. Saying that they stack is a bit imprecise since the claw and the spell are technically dealing damage separately.
I always recommend THIS GUIDE for new players looking into touch-spells. It's most useful for a Magus player, but touch-spells can be confusing for anyone, so it's helpful for any caster really.