Without the gauges, it is difficult. Without the gauges and without a lathe, it is much more difficult.
The easiest would be to contact Brownells and buy headspace gauges for a 223. Better yet, go to a gunsmith and have it checked. You're not going to get a numeric reading from anyone. Noone would have the gauge equipment for that. What they will do is take a "Go Gauge" and put it in the gun. If the bolt closes, that's ok. Then they take a "No Go Gauge". Put it in an if the bolt closes that's no good. It's that simple.
The actual number would be some ridiculous 4 or 5 decimal value, at an arbitrary location on the shoulder of the case that represents some given diameter's distance from the bolt face. Not an easy thing to measure. To be honest, I have doubt about how close the guages are ground. If they are no closer than all the other gun stuff I've seen in my days, I wouldn't put much faith in it.
Moreover, who would care as long as your cases go in your gun. After the days of shooting factory ammo, YOU are the person who dictates the headspace of a cartridge anyhow. The actual numbers are meaningless from gun to gun and it only matters that they are inside a given tolerance. (It's kinda funny when looking at a reamer print that has values to FIVE decimals and a tolerance of +-.003 or 6 thousanths total. What a joke. As if they could grind that anyhow, much less cut to it).
If you have something that you disassemble and reassemble enough times, sooner or later, you'll have two!