Which should be first, pressure reducer or backflow preventer?
I say BFP first.

The backflow preventer must be installed before any point in the system where the line becomes "open" to the introduction of pollutants that would make the water unsafe for drinking (fertilizers, pesticides, herbicides, animal wastes, bacteria, and other things you generally find in your topsoil). While a pressure reducer's basic operation (most are similar to a gas regulator, where a spring-driven piston controls an inlet) is generally "closed", most designs also have overpressure reliefs that vent liquid from the regulator in cases where the "downstream" pressure becomes dangerously high (freezing temperatures, or conversely overheating). This relief valve opens the regulator (and the water in it) to the introduction of pollutants, and so it must be "downstream" of the backflow preventer to safeguard the potable water supply.

Now, as SteveR said, if the pressure reducer is designed and intended to regulate the pressure to the entire water service (reducing the pressure from the mains to a safe level for home plumbing) then its design will ensure that it cannot introduce pollutants in any situation (usually it won't have an overpressure relief) and so it's safe to place in front of a sprinkler backflow preventer. However, if this is a reg for sprinkler systems (i.e. drip irrigation) then it must come after the backflow preventer for the system.