What's a suitable sealant for the garden slabs in the picture?
It appears that there is grout in place now with some caulking where it's cracked out.  I'm going to guess that these bricks are set in a sand base? If so, then you'll never get the blocks stable enough to keep the grout from cracking.

Have you considered just removing the grout and applying some "paver sand" into the gaps?  That's a lot more forgiving than grout and a lot less trouble to maintain.

Otherwise, you'll probably want to go ahead and re-grout this after removing the old and cracked parts.  It will need to be updated regularly but I think the result will be better than just applying caulk or silicone sealer.