Read up on Simple green. I have read in more than one place that it is corrosive. Kerosene is a good cleaner and it's no where near as flammable as gasoline, or Diesel. Diesel is an excellent penetrator also, the equal or better of Liquid Wrench. If you are going to clean something, then immediately apply some type of oil, it's a lot less important what you use though. I mean even WD 40 would clean really well. People say don't use WD 40 because (they say) it dissolves the oils but it does displace water and if you replace it with oil immediately, it wouldn't matter. Note it you have a chain covered in oil and you spray WD 40 on it, yes the WD 40 will thin out the oil and you will have less protection, but it you just re-oil it immediately, it's fine. Again, read up before using simple Green. There may be a newer less corrosive formulas of it out there now but everything I have read (recently) points to it being fairly corrosive. If it was me (using a chain cleaner), I would probably use kerosene or diesel, which ever was easier to obtain, then apply oil soon after.
Currently I am removing my chain, washing it with paint thinner, then soaking it over night in 80/90 wt gear oil that has been heated to around boiling point (yes, i heat it up outside as it stinks when you heat it up). That makes the oil real thin and I swish it around to get the oil in the pins. The following morning, I hang the chain to drip dry followed by a wipe down with a rag lightly damped with thinner to remove any surface oil. At this point any oil on the surface is only going to attract dirt. You want the outside surface of the chain as clean and dry as possible. Basically it takes me over night and to the following evening to clean a chain. A bit longer that you will spend doing it with a chain cleaner.
You are using a chain cleaner and using diesel or Kerosene cleans it and actually has a lot of lubricating qualities in it, just like oil. I would consider using thinner before using simple Green but I don't know if the plastic casing of the chain cleaner would react to the thinner. same thing goes for the diesel or kerosene.