I recently purchased a cylinder of MIG shield gas (argon/CO2). Can I use my existing flux core wire and the MIG gas together or do I need to buy solid wire?
Maybe, but best not use the gas. The flux core has deoxidizers in it like aluminum , silicon and manganese ( not really a deoxidizer). They are expected to react with oxygen from the air and be consumed. If the oxygen is kept away by the gas some of those elements will dissolve into the molten metal . This will add alloys that may affect the properties of the deposit . Many years ago Lincoln did something like this and the resulting welds had high silicon and manganese causing them to be too strong.
Dual shield wire is a different animal than regular flux core wire. You can use gas with regular flux core, but it is a total waste of gas. The flux in dual shield wire doesn't shield the weld, it causes better deposition rates and weld characteristics in the weld. Gas is needed with dual shield to shield the weld, but not with flux cored. So you can use reg flux core with gas, but you cannot use dual shield without gas. Dual shield is generally used for heavy fabrication, allowing a mig style process to really cram the welds in. It provides better penetration, and and less spatter, than flux core alone. Dual shield is also good for heavy fab out of position welds, because the flux that is in dual shield helps the weld pool freeze a bit better. Using gas with regular flux core wire offers no benefit.