They may cause 'lifting' as the roots thicken and push upwards. Where I work there is a birch which has done just that and surrounding flag stones are now quite dangerous.
A gardener's work is never at an end - (John Evelyn 1620-1706)
No, if the kerb is substantial and well constructed it's unlikely to cause damage IMO. Flags and paving stones, potentially yes, as they don't present any real resistance to being lifted. Even then it would have to be quite a mature tree.
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6 feet?