The small filler hole (I don't know what else to call it) that is at the bottom of the bowl, right where the drain portion begins, appears to be "salted up", that is it looks as if it is partially blocked, most likely by growth of "salts" or other precipitation from the water/waste combination. Is this the likely cause of poor flow?
I propose to test the main drain line by pulling the toilet, and pouring a bucket of water down the drain. If this tests ok is it possible there is something wrong with the vent stack (located in the wall immediately behind the toilet) that is easily diagnosed? If the bucket of water test fails I'll snake the drain.
My best guess is the "vent" in the toilet bowl. If this is the case, is this easily cleaned out, or is getting a new toilet the best plan?