Currently, I have Mercurial as my version control in Kiln server. I want to migrate my code to Bitbucket server with Git. I have tried the import option available in Bitbucket but I can only import as a Mercurial repository.
Is there any possible way to achieve this?
You probably need to do the Mercurial -> Git conversion on your own machine with a tool like fast-export.
You then create a new repo on Bitbucket and follow the instructions to push your project to it. You shouldn't hit any major roadblocks.
This answer will give you further information on how to do it.