When you start an Amazon EC2 instance, you must select an Amazon Machine Image (AMI) that is eligible for the AWS Free Tier. Because of licensing restrictions, some AMIs aren't eligible for the AWS Free Tier.
It's also stated
To stay within the Free Tier, use only EC2 Micro instances.
Are some community AMIs eligible for the free tier if they are open source and can be run on a
Edit: It seems it might be the case that some are eligible, as a comment in the AWS forums states:
There are some community AMI's that are eligible for the free tier. You can see these by selecting the AMI, and then looking at the available Instance Types. If there is a "Micro" option annotated with a star then it is eligible.
Moreover an answer on SO also explains this could be true.