Neither Infernal Influence nor the 3rd level Infernal bloodline power say anything about improving your existing fire resistance, so you just get the better of the two. The question of stacking does not come up because neither of these items is described as any sort of bonus.
At my table, I would probably let a player replace the Infernal Influence trait when it becomes redundant at 3rd level.
It's a difference between gain/grant and add.
If an ability grants X resistance, that's what you get. If you have it from multiple sources, the highest applies. For example, if you cast Resist Energy (Fire) at level 8 on yourself, you only get fire resist 10.
Compare to the human paladin alternate FCB that adds to any resistance of your choice or the magic trait Unscathed that increases your existing resistance by 2.