Below are comments (that have now been removed from underneath the original question) I believe contain helpful and useful information that relate directly to the question asked.
@wax eagle comment from above:
For sure don't use salt. Too much salt will make it so nothing grows. But it also dissolves in water and can therefore travel into areas where you do want plants to grow.
Salt also isn't a good answer in your case ie hard landscape, due to erosive effect it can have on concrete, stone, etc. For a drastic image, think about the damage salt (especially old school salt) has on roads, bridges, etc each winter when it's putdown to clear ice & snow.
@Mike Perry comment from above:
Stay away from vinegar based herbicides where concrete, stone, etc will come into contact with it. Why? The acidity in those types of herbicides will eat into the concrete, stone, therefore having a negative affect on them.
Below are 3 organic options that will not have a negative effect on your hard landscape:
- Herbicidal soap sprays (a quick internet search will turn up homemade recipes & off the shelf products).
- Hand-pulling, cheap (basically free, apart from your time), effective, and very easy to pull them up after a good downpour.
- A small propane-powered flame weeder.
If you want to go with a herbicidal soap and would like some more information, report back, and I'll (and I am sure others can/will) add in more information on that option.
Home made Herbicidal soap recipe (for use in a hard landscape):
- Warm water
- (Eco-Friendly) Liquid dish detergent, from 0 to 20% (do NOT use dishwasher or hand soap)
Seeing as you are not too concerned about what you kill within the joints of your flagstone, I would start out with a 5 to 10% concentrated mixture, and see if that works (it should do). If it doesn't, you can always mix up a higher concentration and try again.
I would apply the mixture with a spray bottle, so that you can specifically target the weeds you want to get ride of. I personally wouldn't go about just spraying "anyway & everywhere".
Spray the weeds, then 3 or 4 days later go out again and spray them, then again 3 or 4 days after that.
Bear in mind, you will mostly likely have to apply a few application of your mixture before you start seeing any results (hence the above statement).
You might then find, at least for the first year, you will have to go out they and spray your mixture once every 2 or 3 weeks.
But eventually, so long as you keep on top of it, you will most definitely start winning the weed battle. You could end up only having to spray your mixture 2 or 3 times a year (your actual mileage will vary depending on the weeds you have to deal with).
Good luck, and please keep us posted on how it works out for you.