There is no specific procedure for that in the Schengen Borders Code. It's not even clear that stamps are required at all (some countries seem to require them, others don't). So the only thing you can get are regular Schengen exit and entry stamps and you probably want to avoid any dangling entry stamp. To have a coherent series, you therefore need a pair of stamps (exit and entry on the same day), which is undistinguishable from a “border run”.
In that context, it doesn't really matter if it's a land border or an airport. If you go to a Schengen external border and turn around, you end up with two stamps, which is the point (provided the border guards let you back in, of course). The border between Poland and Russia is an external border and border guards will have the necessary stamps on hand.
The only odd thing about Kaliningrad (as opposed to say, Croatia or Romania) is that's it's not so easy to enter Russia. Polish border guards are not in charge of enforcing this but they might still ask you about your lack of visa and must be willing to play along with your plan. I have no idea whether they would.