Absolutely not; SkyPriority does NOT give you extra luggage.

In any case, getting an extra bag on just BHX-AMS (KLM Flying Blue benefit) is unlikely to affect whatever charge EY would levy on such an extra piece of luggage (Etihad probably charge the same amount to carry an extra piece from AMS to MNL as they do for BHX to MNL); in any case, it's Etihad's baggage rules that apply to the entire ticket here. And I genuinely don't think it is even feasible - if you could get the KL check-in agent to grant you an FB benefit for just BHX-AMS - for them to recalculate any additional Etihad fee on that basis.