I'm also new at welding and have just gone through figuring out the same problems you are experiencing. Mig welders with flux core or gas shielding type? The first welder I bought was a Handycore Lincoln 100. (110 volts) As mentioned in the thread the smallest wire that I could use with this type of non gas welder was a .030 flux coated type. Because I am not an experienced welder, results were too much heat & wire to large for this type of sheetmetal repairs. I could not get the settings etc. Because .023 flux coated for this welder did not exist. I sold it and bought a new Millermatic 140 Mig 110 volts welder. (argon gas sheilding)this one can run the .023 wire.
A professional welding shop informed me that for this job, (& the fact that I was inexperienced)to prevent overheating the sheet metal, I needed .023 wire (which is not flux coated)& uses argon gas sheilding type Mig Welder.
I am happy to say the new welder is a pleasure to use even for an inexperienced person like myself. Very user friendly, measure the gauge of the metal, open the cover on the inside and a chart gives me the exact settings required based on the metal thickness,heat range & wire feed rate. Results are , good penetration, nice solid welds, no overheating of the sheetmetal. I am really pleased.
Hopefully your welder has the gas type sheilding.
I'm am not experienced enough to say that the flux wire weld is not possible. But for a non welder person like myself this was better for me.
It was nice to read all the excellent reply's by our fellow Stovebolters. When someone like you asked the question it really helps the new guys.