If you'd like something other than opinion, here is what Comp Cams has to say about it for their flat tappet cams (most every other cam manufacturer is going to say the same): After the cam break-in, then the initial oil change, then you can use synthetic oil in your engine. You need oil which has zinc in it so you don't wipe your cam lobes.

No, synthetic oil should not be used to break in flat tappet cams.