This assumes any inside information is distributed across the set of jet owners relatively uniformly. In reality most of the private get guys run dealership chains or well services companies. Nobody is going to bother tipping them all off.
The reality is, much like American wealth, the distribution is super-exponential. If you actually wanted this to be kind of useful, you'd only look at the tail numbers known to belong to people who are associates of US senators, high ranking congressmen, and senior defense officials (Raytheon/LM/NG/Boeing execs).
That said, the *actual* reality is you'll just fucking know because it'll be obvious things are escalating out of control. The government is not mystically competent, they're morons like us just figuring it out as they go along. If things were to somehow pop off unexpectedly you only have somewhere between 3 and 30 minutes which is not enough time to get an aircraft in the air with no notice.
TLDR this doesn't do anything. It's cool though
There are questions about who would be launching all-out nuclear war on the US when there are such obvious and effective indirect means of destruction.
If you want to destabilise an economy, destroy science and R&D, nuke healthcare, ruin decades of trust with allies, disassemble democratic checks and balances, co-opt the media, and give most of the population a nervous breakdown that has them believing batshit divisive nonsense, you certainly don't need nuclear weapons to do it.