I have a few flat tappet cams I have run fine without additives, on valvoline and Mobil 1. If its not a very aggressive cam it should be fine without it.
The other thing to remember is that ZDDP in itself is relatively meaningless. There are oils on the market that contain close to no ZDDP and can run a flat tappet cam just fine- they're made synthetic replacements for ZDDP.
Its always best to stay conservative (safe) but do some research into what you have and what you need- you may find that all the ZDDP hype is just hype in your case, or you may find it is an absolute requirement and need to get mail order oil.
Be sure to distinguish marketing and "my neighbor's best buddy" stories from facts too. I've heard of some neighbor's best buddies that have done some impossible things...