That is cute!
I have not used that particular machine but I have a Jonsered chain/chisel and I have used the chain a number of times over the years.
First you need to run the chain a little bit slack and keep it oiled. Second is to only plunge cut vertically and never try to cut horizontally. If you need a wide mortice then cut each end and clean out the middle. If your mortice is 1.5 chain widths then the second plunge is always to the right as you don’t want the chain pulling itself down into the cut.
It is ok to flatten the bottom after all plunge cuts but remember the machine is not built for side loads on the chain and bar assembly. Also travel left so the chain does not pull.
It is a bit more of a rough and ready process than a chisel but it is fast. With a sharp chain you can get a decent finish.
How do you cycle the chain up/down? I don’t see any kind of hand lever? Is that a chain going down to a foot pedal?