If you run gas on flux core you won't see any difference at all one way or the other it will just wa$te gas! Some people have confused the cored MIG wires (duel shield) with running gas on flux core but that is an entirely different wire and it requires gas same as solid wire. These wires are usually used in larger sizes than we normally see on the home shop type MIGs but now both Hobart and ESAB have the Hobart Excellarc 71 and ESAB Duel Shied II 71 Ultra available in .035 that works great on these small machines. These wires run good on either C25 or straight CO2 and although not for body work they are REALLY good for fabrication like that go-kart that was mentioned. The Excellarc or the Ultra will run smooth and lay a really slick bead under a slag that will simply brush off, if it does not just fall off by itself, and is a much better wire for building things than the solid types. I especially like the Hobart Excellarc since this stuff will weld vertical and overhead just as easily as flat, a lot easier to weld overhead than solid wire, and will bridge a gap like nothing else!
BTW, to run flux core on your MIG, which you may need to do sometimes, you just switch the polarity to straight (electrode negative, ground positive) and leave off the gas, you MUST switch the polarity! You may need to use the flux core when welding outside for example or in any other drafty situation so it is a good idea to keep some on hand. There is a common mis-conception that in drafty conditions you need to turn up the gas flow, this recommendation is even used in a lot of welding manuals, but this almost always does not work and will lead to poor welds. The thinking is that the draft "blows away" the shielding gas but that is not what happens, what actually happens is that the draft will contaminate the shielding gas and it does not have to "blow it away" to cause damage. If you have problems with porosity due to drafty conditions FIX THE DRAFT and leave the gas alone, you will get a MUCH better weld for your efforts.