I think the photo
IS of the flexible coupling, but I agree with CSY
Get the source of all that corrosion
before you launch, and replace those bolts. The stuffing box is the #1 suspect.
If you can afford it, replace the stuffing box with a dripless seal, they're great. Zero water
leakage, one time adjustment, and no shaft wear.
The coupling is probably OK if it is plastic, but if those end plates are spongy, chuck it.
The engine alignment is done with the motor mounts. They can slide sideways and the studs have threads which allow each corner of the engine to be adjusted vertically as well. The goal is to make sure the engine is aligned both vertically and laterally with the shaft (which needs to be held in the center of the stern tube while checking all this).
The mating surfaces of the flanges should line up evenly when brought together. Something like .010 runout is acceptable as I remember.
Get it in the ballpark when the boat's out of the water
, then after launch you can motor safely until you can let it set for a few days, then do the final.