+1. Gotta see what you are seeing. The answer is pretty easy and Joseph is correct. Caulking does not = flashing

Added some pictures. Sure, I wasn't intending the caulk to be flashing, just an added measure. I was thinking something like vycor applied over the gap might act as flashing, since I didn't know how you could 'flash' a vertical surface like that. But that's was just a first guess... definitely why I'm asking.

For what it's worth, the little concrete pad landing pad outside that door is pitched away from that corner in both directions. But unfortunately chipmunks have managed to get into that corner (they are no longer with us) and there is no longer concrete directly under that rotted 2x4... I can stick a screwdriver down into dirt. I won't really know exactly what's going on there until I pull the door. The rest of the wall on the other side of the door is just a 2x4 wall with an untreated sill plate on-slab and it looks good as new from 1960. Just this corner is a mess.

The top and the sill are the most important and I would address those as well.I would foam or caulk the joints if they to small to foam between the door frame and studs and perhaps where it meets the concrete, you could also run a bead between the studs. You then use a flashing tape over it all but it won’t do much good and can trap water if the top is not done . If the door is remaining I would probably not worry to much about the sill, but the sill would typically be done first then the sides the top.

you Could also use a liquid flashing.