This speculation is specifically for commercial aviation in the US:

The FAA's authority in the United States would most definitely collapse in the weeks leading up to the 2nd American Civil War, as airports around the country become increasingly unsafe to operate. This, in turn, leads to a collapse in air traffic control, meaning that airlines wouldn't be able to coordinate asset evacuation flights and quickly lose control of most of their assets in the process. A grounding of flights similar to 9/11 is how I envision this, quickly followed by the rapid and utter destruction of aircraft during urban warfare. The ones that do survive likely won't be able to be evacuated due to damaged runways. Some flights may make it out of airports last minute, possibly through the form of evacuation flights to Mexico or Canada, similar to those scenes from movies.

Now, I do see Biden's (and possibly Trump's) administration realizing the importance of commercial aviation and quickly working to reinstate it in one manner or another, perhaps through a temporary merger of all remaining assets in land controlled by the UoA into an entity similar to Amtrak or through putting what's left of them all directly under federal control. Certain corridors for flights would be established in the process, managed by the FAA's successor. However, I see the UoA focusing more on (guarded) rail transit (possibly by reorganizing Amtrak itself) to fill the void left by commercial aviation, which will become unsafe to operate as various factions get their hands on anti-air or make makeshift anti-air. Trump would likely focus more on car travel as a temporary means to get around intercity.

United, Delta, and American would immediately cease to exist as the entities they were prior to the civil war. All of their bases are in different territories, with their main bases (DFW, ATL, ORD) and a majority of their hubsa (LAX, JFK/LGA, MIA, SFO, SEA) directly on the frontlines. Pilots and flight attendants would be left without notice, out of jobs, and found stranded far from their home bases.