If you are using a full sheet of acrylic, place a rail on two adjacent sides on your cutting table. It could be as simple as bolting scrap to the table, then cutting away that which is out of bounds of your cutting head. Anything placed firmly against these two rails will be in exactly the same place for each action performed on the work piece.
When you flip the material over, it will be in a known location, but you'll have to ensure that your inkscape files are properly aligned (also known as registered) with the flip.
You can create files with registration marks outside the token area to use as alignment assistance while creating the templates for the tokens.
If it's not obvious, your engraving will be done on one side, then the material flipped and engraving and cutting on the second side. One hopes you don't have such thick material that it requires dual passes to cut through.
The alignment rails need not be outside the range of your cutting head, but you will want to secure them first, then cut them for more precise alignment considerations.
One way to go about this is to create a rectangle in inkscape. This is the guide cutting rectangle. Use this rectangle to also create the token images. When you use Inkscape mirror/flip feature, you'll be able to see how well it aligns. You may have to add compensation for kerf, the material removed by the laser, which can be 0.100 to 0.200 mm depending on the thickness of your material and the power setting of the laser.