What is the common way to deploy a chart(which contains sealed secrets) to different clusters?
Because the clusters contains different sealed-secret controller (with different secret key) it seems unfeasible.
Or is there any way to install a sealed-secret controller with the same secret key as the other clusters?
Sealed Secrets can be created by anyone but can only be decrypted by the controller where the secrets are created, follow this blog authored by Vidushi Bansal for more information. So in order to use sealed secrets for multiple kubernetes clusters you need to maintain helm directories or repositories and set the target clusters as described in this solution provided by seshadri_c. Now since these sealed secrets have respective target clusters it will be easy for you to manage multiple clusters.