STP does not list the ZDDP content of their additive on their website. I would prefer to use oil that had the correct amount of ZDDP to start with, like the Valvoline VR series of oils.
For engine break in I use the GM EOS or the cam manufacturer supplied additive like Chuck mentioned w/Valvoline VR oil. I then change the oil and filter and run straight Vavloline VR. No trashed cams as of yet.
In regards to synthetics with a flat tappet cam, I can only tell you this:
I called Royal Purple and actually got a real person on the phone. They did not recommend that I break in an engine with their oil, but they said it would be fine "to use their product after about 2000 miles". Valvoline VR oil is cheaper than the RP stuff and I never have to worry about ZDDP content.