Hello EzBrEzPSM,
One role I used to fill for my employer was that of Logistics Manager, so hopefully I will be able to help a bit, but need more information.
How many rolls? How far are you having it shipped? How fast does it need to get there? Do you have road cases or anything available for protection? Where are you located?
In terms of shipment prep, outside of road cases I can't really think of a fail-safe way of providing some protection. You could also build cases out of wood.
One challenge with vinyl flooring is the rolls are typically larger than a 48x48 pallet, which can make LTL (Less than Truckload) shipments risky. You don't want things bumping up against the rolls, especially the edges, as it could damage the flooring. If you have road cases (which I doubt as by asking this question it doesn't seem your company is tooled for touring) then throw them on an LTL shipment and you're set. With LTL shipments your freight is consolidated with other LTL shipments. If you're shipping less than 10 pallets, LTL is usually cheapest. LTL will also take the longest, as your freight will go between depots or distribution centers for consolidation.
If you have enough rolls it may be cheaper to do an FTL (Full Truckload) shipment. I doubt you are shipping that much, but important to differentiate between FTL and LTL shipments. In this case your freight has a dedicated trailer, nothing else is on it and therefor you mitigate the risk of damage. You don't necessarily need to have a FULL truckload for an FTL shipment to be the best option. With LTL the cost is increased a bit as there is more work involved for the carrier with LTL. If you have half a third trailer load or more you may find FTL to be a better option both financially and operationally.
Both FTL and LTL would be for non local shipments. If you're staying in the same region, check regional freight lines as they're usually cheaper than the national carriers. If you're staying very local (~3 hour drive) you should look into a local courier or delivery service. They'll have box trucks that could be dedicated to your freight.
One final note, and not to directly contradict Nick below - but UPS and FedEx freight are usually considerably more expensive than a trucking line. That said, they're definitely viable options and can get the job done.