Silicone is a flexible, long-lasting and highly adhesive sealant that's highly waterproof and easy to clean up. Its flexibility means it can be squeezed and bent into many different shapes without cracking or breaking under the strain. A stronger adhesive is needed for a driveway because it will be walked on regularly and parked on for extended periods.
External grouting needs to rate at least 35 on a Shore hardness test if it's to withstand the force exerted on it by a woman of average weight in high heels. The Shore hardness scale is a measurement of resistance to indentation of a material. Because silicone is soft and doesn't usually reach level 35 on the scale, it's not recommended for driveway grouting.
Concrete driveways need grouting that can breathe to expel moisture from the concrete and earth beneath. As a non-porous sealant, silicone doesn't breathe and is inappropriate for use on concrete driveways. Using silicone also creates a film on the concrete surface.
The best alternative to silicone as grout for the driveway is mortar with a high sand content in comparison to cement content. A 3:1 ratio provides the porous medium that flagstones require while also having good bonding qualities to hold the flagstones together and rate highly on the Shore hardness test.