Where should migrations be run on elasticbeanstalk deployment process?

You can try the flag: leader_only in an ebextensions configuration file. This flag will make your migration run just once even if you have the app deployed in many instances. For example, save this file into the root directory of your project at the path: /.ebextensions/migration.config

option_settings:
container_commands:
    database_migration:
        leader_only: true
        command: "db migrate"

More information: AWS Elastic Beanstalk Official Docs

As the OP didn't specify the platform, I thought I'd add a specific .ebextensions/migration.config config for Ruby on Rails, as I encountered this exact issue as well:

container_commands:
  12migrate:
    command: rake db:migrate
    leader_only: true