Does BGP dampening need to be configured on both ends of neighbor ships?
Will it work if I only enable it on my end and not on the ISP end?
BGP dampening is local to the router, it doesn't depend on a configuration on the neighbor router.
But if you are an end customer it is of little use unless you use extensively BGP inside your own network.
And still, the usefulness of BGP route dampening is questionable.
In this report a RIPE working group state that:
As the power of routers has increased, the original needs for BGP Flap Damping is no longer a major concern for operators or router equipment vendors as it was in the mid-1990s when route flapping consumed a signficant percentage of the CPU of early routers. In fact, the negative effects of RFD, as described above, have become the major concern, the cure has become worse than the disease!