I'm trying to build a class in Pathfinder with the Bloodline Class Feature. I need to know, could I Enhance my claws with for EX: Flaming, even if they're natural weapons?
Only if they are masterwork
To create a magic weapon from a mundane one, the weapon must first be of masterwork quality. Natural weapons generally are not of masterwork quality, and the quality of a weapon generally cannot be increased once the weapon is crafted. That said, you may be able to craft new claws (or other natural weapons) with an appropriate crafting skill, or potentially purchase or start with masterwork ones, depending on your GMs campaign (q.v. Can a monk's unarmed strikes be enchanted? , recalling that unarmed strikes are not natural weapons).
An Amulet of Mighty Fists is the usual method
An Amulet of Mighty Fists serves the same purpose for natural weapon users that purchasing magic armaments does for manufactured weapon users. Unless you are monk trying to double dip, there's little reason to upgrade the weapons themselves individually rather than the amulet which provides the enchantment to each natural weapon you possess for the same cost.
Given that "Enhancement" is a pretty broad term covering all types of effects on natural weapons (claws in this instance) you may find some of these suitable.