What would be the reaction equation between ammonium nitrate and a powdered metal?
I'm betting they mean that you can inadvertently make an explosive (technically a blasting agent) or highly flammable mixture by mixing powdered metal and ammonium nitrate.  I used to be a hard rock miner many centuries ago and was well read on explosives.  Aluminum powder and ammonium nitrate is a classic solid rocket fuel and industrial blasting agent/military explosive, for instance ammonal in bombs.  Ammonium nitrate/aluminum powder mixes (magnesium works, too) have better explosive properties than the usual mining ANFO (ammonium nitrate/fuel oil) mixtures, but the latter are preferred usually since ANFO is less expensive.

While blasting agents technically need a booster explosive to detonate, they will burn ferociously.  I'm guessing when a writer of a SDS sheet talks about powdered metal and AN, they are thinking about the potential of creating an extremely flammable mixture.

I looked at some MSDS for ammonium nitrate, and I see powdered metal listed along with reducing agents as incompatible mixtures.  Could you post a link to the MSDS you are reading?  I'm interpreting 'incompatible' as referring to explosive potential and not to a slow spontaneous reaction.

EDIT:  Well.  The usual metal powders that react with AN used in mining and explosives are aluminum and magnesium, so that is all I considered.  However, a bit of research shows that powdered zinc does react with ammonium nitrate, as in this video (note that it didn't actually ignite until set afire, but it definitely reacted).