cross account ssm start session

Thanks James. This addresses my concern.

However, is there any other way how we can define the Assume Role option. As far as i know, through CLI we need to fetch the sts credentials to temporarily assume the new role.

if we can make it seamless by just defining the same in say Account B's role's trusted identity section or something. I mean just wanted to know if there is some way where the user trying to establish the session just needs to mention the instance ID and they are done

There's a feature in AWS CLI (which also works for the SDKs) where you can specify in a profile that it should be automatically assumed from another profile. For example, you could create an "account-b" profile, which will automatically use "account-a" to assume it. Then you can just specify --profile account-b for your command. The configuration option is source_profile; see the docs here for more: https://docs.aws.amazon.com/cli/latest/userguide/cli-configure-role.html

Adding (having re-read your comment) that beyond the role assumption part, you would need some logic to find the right account for an instance ID, which could be possible with something like AWS Config Aggregator as you could query it (including via the CLI) for the account ID for a given instance, and then have a script select the correct profile based on that. Docs for Config Aggregator are here: https://docs.aws.amazon.com/config/latest/developerguide/aggregate-data.html