You are safe to keep MagMod Grips and accessories on your flash at all times. You might need to remove the MagGrip from your flashes to fit in a smaller bag, but we actually keep our MagGrips on each flash inside of our bags. This makes sure our flash is always ready to use without the need to put the MagGrip back on the flash.
We recommend using the MagMod Carrying Pouch (available with the MagMod Basic Kit, the MagSphere, the MagBounce, the MagSnoot, and the MagBeam) to store your MagGrid, MagGel, as well as your MagMod gels. Please be aware that magnets can harm magnetic storage devices, like hard drives in older laptops. If you typically carry a laptop with your photography gear, check with the manufacturer to see if it has a SSD (Solid State Drive) hard drive. These are safe around magnets, but older 'optical hard drives' are very sensitive near magnets, and you could potentially lose data.
For more information check out our support article about magnets: https://support.magnetmod.com/hc/en-us/articles/115004213747-Will-magnets-damage-my-camera-gear-