A civil war would have more issues behind it than gun rights.
By your logic there never should have been a successful civil war in the history of the world, since the govt always has the military and police on their side. What you are imagining isn’t the real world.
Well, no, if it’s a proper civil war, and not an insurrection, then usually you have the military divided between the belligerents. The English and US Civil Wars are good examples of Modern Era civil wars. In both cases you had two armies (well, okay, technically in the English Civil War there was also the Scottish, but I digress), and thus some degree of equality. In other words, both sides could field armies and fight conventional battles for their time.
Assuming the US military stayed loyal to the President, all the gun owners in America would still end up being little more than a very large insurrection, and while it might be able to fight some sort of guerrilla campaign like the Spanish partisans did in the Peninsular War, it would have no hope of any real victory. But warfare and the technology behind it has changed significantly since even the Peninsular War. Then, it was conceivable for even irregular army to have weapons at least somewhat similar to the weapons available to the regular army they were fighting, but modern militaries, particularly the US’s, are so far beyond that, that it’s hard to imagine what you think a bunch of civilians are going to hope to accomplish.
For there to be another US civil war there would need to be some significant portion of the US armed forces splitting from Federal control. All the civilian guns in America would not make a civil war. The Second Amendment, at least so far as it is rooted in the notion that the people might need to battle for their liberty against tyranny, ceased to be plausible scenario even by the mid-19th century. By that time, even the combined might and manpower of the Confederacy, with some pretty talented generals, was unable to defeat the Union.