Eating egg shells feels very unnatural, hence I'd be very cautious.
I performed an experiment to see how easily absorbed egg shell was. I ground egg shell to a particle size of around 0.25mm with a mortar and pestle. This was as small as I could get it after around 15 minutes. This is probably in the area of course ground pepper.
Once done I took a teaspoon of the powder after a meal and swallowed it with the help of a quantity of water only just sufficient to wash it down.
A day later, in my stools I observed pieces of egg shell identical to the ones I swallowed. Neither smaller nor rounded.
Conclusion: The egg shell was not dissolved by my gastric acid. Due to its jagged appearance, I'd say it wasn't even partially dissolved (one would expect it to be rounded at least). There is only one explanation for this: The fragments of eggshell visible in my stools were washed out of the stomach before they were acted on by the gastric acid.
Now particles of eggshell are particularly course and brittle, an abrasive combination and from my experiment I can clearly see at least part of the powder is getting through my stomach undissolved... Whether it is doing damage to the delicate intestinal lining as food is forced through the intestine, I'll leave for you to consider.
I've demonstrated that is is possible to wash egg shell straight through your stomach. If you wish to take eggshell, a particularly abrasive substance, then take caution and make sure it is actually being dissolved in the stomach. Whilst egg shell ground to a much smaller particle size would be dissolved far quicker, for it has much higher surface area, it wouldn't matter if it is still being washed through immediately.
Grind it into the finest powder possible
either a) consume with something that sits in the stomach for a long time, eg, solid food, particularly meat
b) pre dissolve the egg shell in something like vinegar (though drinking vinegar is going to be rough but good luck)
Perform your own experiments and use your own logic and reasoning. I'd seriously ask someone with credentials before you start eating egg shells if you have any doubts.