First, it appears that this gets rid of the cosmological constant (which some people seem to have an aesthetic aversion to, but there's no reason it shouldn't exist) by replacing it with 'both a varying gravitational “constant” and a varying speed of light'. In other words, it appears to make the model more complicated and less aesthetically pleasing. Skimming the article, the author appears to make a fairly arbitrary seeming argument about how those constants ought to vary with time which simplifies things a bit, but it's still more complicated than traditional GR with a constant c and G.
It's not clear to me how this model purports to solve the flatness problem. There just seems to be an assertion that because the model predicts a 3-sphere geometry that the flatness problem is moot, but that seems to dodge the question. The whole point of the flatness problem is that space appears to be flat, and not a 3-sphere or hyperbolic. If you say it's a 3-sphere, the problem becomes why the universe ought to be so big that the curvature isn't apparent.
Similarly, the claim to solve the horizon problem is unsatisfying. Most attempts to explain the horizon problem require you to assume that the universe was once much, much smaller and expanded very rapidly at some point (inflation). This model appears to give you a knob to do that (variable speed of light), but doesn't really say why it should have evolved in that way.
Finally, there are some red flags to be had here from observing that the author works in the statistics department, appears to have never published any previous physics research, and in 5 months has not gotten this paper published in a peer reviewed journal and has not been cited by any other work.
Bottom line: I wouldn't put much weight on this.