I know there has been confusion with the launch of Inquisitor, and the auras of these ships, as well as their existing Bloodthirst abilities, so let me clarify a few things.
TL;DR: Bloodthirst bonuses only effect the ship generating them, Rival Aura's effect all other Rival's including itself.
Each time a ship with "Rivals - Bloodthirst" makes a kill, all ships with "Rivals - Bloodthirst" gains a stack.
This ability ONLY effects the ship generating it.
These ability increase with each stack to a max of 20 which is described in the blue print.
Each of the Rival ships produces an aura which effects all other rivals in the fleet (example: Incinerator grants +1500 Corrosive Deflection)
The ship that generates this aura is also affected by it. (example: each rival hull in a fleet with an Incinerator gets +1500 Corrosive Deflection, including the Incinerator generating this aura)
Having two of the same same ship does not double this bonus. (Example: 2 Incinerators in your fleet will only grant +1500 Corrosive Deflection to other rivals in the fleet)
Points of confusion: