My first recommendation would be if you just bought this thing is to take it back for a refund. Reason: Mig welding (with gas) or fluxcore welding (without gas) are both DC only processes. I believe if you look at the output sticker on your welder you will likely see it is an AC output machine. Nothing wrong with an AC output on a stick welder as there are welding rods designed to work with AC output in stick. That said, there is not a fluxcore welding wire made designed to work with AC output in a wirefeeder as again it is a DC only process by nature. (Read directions on any wire you purchase to put in that welder it will say DC only).
Not saying it will not melt some metal together but it will never weld well. There are other cheap alternatives to be had in 115 volt wire feeders that output the proper DC type voltage but they will cost more than the $99 to $150 that this level of doorstop sells for.
If you dead set on keeping it, well what works the best on it may be totally different than what most people use on their DC output machines. My little Lincoln SP-135 mig (115 volt mig) , I simply take the gas nozzle off to run fluxcore (and of course switch the polarity). If I ambitious I have a rubber tip I slide on there too to protect gas nozzle threads, but it is not required. I have even used Teflon tape to protect the gas nozzle threads when I could not conveniently find the rubber tip.
I'm pretty new at this welding forum. Glad that you took the time to explain & post the requirements necessary to weld with the mig & fluxcore. Read a reply to this matter a week or so ago that was posted to this Forum. It was probably yours but I was unable to find it until you reposted it. I contacted Jobsmart - They are full of selling a lot of Buffalo equipment. Not sure what part of the Buffalo I was talking to.

All I was able to determine is that it is an AC output machine as well as several other fluxcore, low end welders, harbor freight, etc.
It was suggested to use fluxcore wire that is available. Which I have! OK, with that said an as you pointed out it does work somewhat. Please don't take this this the wrong way

. I watched a few Harbor Freight videos using their FLUXcore to weld rather thick steel plates together. 3/16 - 1/4 - 3/8 & even 1/2" plates. Not pretty but fairly well done. Not a one pass adventure but workable.
With that said when I purchased the Jobsmart 135 I had no idea, these prototypes were designed for AC to me, what the hay, a welder is a welder. Your posting has serve to clear the AC DC issue. Also , as far as I can determine the polarity is set on the Jobsmart. Where as your lincoln SP - 135 will do what you want to.
Just purchased a new Hobart 140 and really wanted to keep the jobsmart to weld thicker plates. While setting up the HB with sold wire for doing thinner sheet metal 24 gauge or similar as the Jobsmart for me, just doesn't do sheet. Thanks for taking the time to help this SC understand what's going on. I like the picture of the tip on your SP-135 I may be able to tweek the present set up to work satisfactorily. Maybe an AC fluxcore wire may be available that we don't know about? KK USAF 62-66