Hi Linzi, welcome to Social Slimmers!
My strict SW advice is that they are not syn free.
Although you would make them from a potato, which is a free food, they are classed as a tweak.
SW says that because you use a free food to make them, it would be really easy to overeat them rather than reach for the speed foods, and you are meant to syn them at the same value you would normal crisps (6.5 syns per 25g of Ready Salted Walkers!)
My 'been a member for many years and have seen hundreds of people on the plan' advice is that you can make them, but if you start to notice your losses reducing, or turning into maintains/gains when you've otherwise been completely 100% on plan, cut them out.
Some people don't syn things like Avocado becuase it has great healthy benefits, and they eat it maybe once a fortnight (or less) and they don't count the 9.5 syns per 100g.
But the advice is always, if it starts to effect your losses then stop thinking of them as syn free and add them to your syns.
Does my rambling make sense?