No, it doesn't stack.
In most cases, modifiers to a given check or roll stack (combine for a cumulative effect) if they come from different sources and have different types (or no type at all), but do not stack if they have the same type or come from the same source (such as the same spell cast twice in succession).
If the modifiers to a particular roll do not stack, only the best bonus and worst penalty applies. Dodge bonuses and circumstance bonuses however, do stack with one another unless otherwise specified.
Bonuses in pathfinder never stack if they are typed, unless said so otherwise. And they certainly do not stack if they are from the same source, even if the bonus is untyped (Again, unless it says it does).
This ability says you enter a state similar to a barbarian's rage, meaning that you cannot enter this state twice for double the benefits because the ability does not say it can stack with itself.
The bonus you get on your barbarian's rage is on top of this Blood Vengeance state:
If you have the rage class feature and are already raging, your morale bonuses to Strength and Constitution increase by +2 for the duration of your rage.
Which means that Blood Vengeance increases your barbarian's rage by 2 points If it was +4 it becomes +6, if it was +6 it becomes +8, and so on.
So you are attempting to stack this Blood Vengeance state with itself multiple times, which the feat does not say you can do, therefore, you can't.
In this ability's case, the ability does grant a benefit if another ally falls while this ability is in effect:
if another ally falls before this duration ends, the weaker rage lasts for an additional 4 rounds.
Bonuses are numerical values that are added to checks and statistical scores. Most bonuses have a type, and as a general rule, bonuses of the same type are not cumulative (do not “stack”)—only the greater bonus granted applies.
The important aspect of bonus types is that two bonuses of the same type don't generally stack. With the exception of dodge bonuses, most circumstance bonuses, and racial bonuses, only the better bonus of a given type works. Bonuses without a type always stack, unless they are from the same source.
The bonus from Blood Vengeance is not on any rolls, but a untyped bonus on your morale bonus from Rage, it increases your morale bonus. Which works exactly like enhancement bonuses to armor class, which increases either the armor bonus or the shield bonus (a +3 light shield actually grants 4 points of shield bonus), and do not stack with any other enhancement bonus (only the highest should apply). So even if you had multiple sources of this Blood Vengeance bonus, only the highest would apply.
Another example that enforces this ruling is the spell Ray of Enfeeblement. The source of this penalty is the spell, even if it is cast on the same target by multiple casters, only the highest penalty should apply.