You could try vinegar. It won't kill a perennial weed (like dandelion) but it will kill the top growth, and if you keep after it - spraying every time it regrows - you might exhaust the root to the point that it won't come back. It will kill annual weeds. I would think that salt would work as well, and if you don't have a big area to cover, it won't make a heck of a difference when it washes into the storm drain. Don't put it near trees, though.

Boiling water should do it. But new seeds will find their way into that crack and sprout up. So unless that crack is "caulked" some way, something will sprout occasionally.

Since no plant can grow without soil there must be some there. Dust from the air settles into and fills in most any crack in asphalt and concrete and then plants start to grow. Hot water, does not necessarily need to be boiling, can be used and while somewhat hazarous is not nearly as bad as some of the plant poisons. Pickling Vinegar can also be used and is best if sprayed on during the heat of the day, in bright sunlight.
But the most effective method of keeping "weeds" from growing in those cracks is to periodically clean out the accumulated soil that is in there.