Hard to find oil with zinc in it anymore and thus a big cause of cam failure on newly rebuilt flat tappet engines.
Modern oils have the same level of ZDDP as oil did in the 50-60s.
ZDDP is being replaced because there are other additives that do the same/better job...high ZDDP levels prevent oil oxidization.... not wear. High ZDDP levels actually destroy metals.
API has a specific test for flat tappet wear... the API spec for tappet wear started in 1959:
This test technique was accepted by Section G-IV of Technical Committee B of ASTM Committee D-2 in October, 1959 as Test Sequence IV. This test was one of a series of test sequences to be used for evaluating oils for API Service MS.
You can read about it
HERE even has pictures!!!!
So any API current spec motor oil will be fine for flat tappet motors (which are still made by the millions.. called inverted bucket lifters).
If you have a HIGHLY modified race engine (double springs, aggressive cam etc) then you might have a need for high zddp levels.... but at that point you should be using roller followers and rockers.... which need little to no ZDDP.
So yeah... any API oil is fine. Specialty/Race/custom blends do little for a stock/warmed over motor. Pouring ZDDP into your oil is completely useless... unless its part of the additives package it will not emulsify nor 'stick' to the wear surfaces.