Exporting RDS DB Snapshot from one account into an S3 bucket in another account

Yes, that is possible. In Account A, create an IAM role with permissions to access the RDS snapshot and the necessary S3 bucket in Account B. This role will be assumed by Account B when exporting the snapshot using the CLI with aws sts assume-role and aws rds export-db-snapshot.

The policy in Account A would look something like this:

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Sid": "AllowAssumeRoleAccountB",
            "Effect": "Allow",
            "Action": "sts:AssumeRole",
            "Resource": "arn:aws:iam::ACCOUNT_B_ID:role/ROLE_NAME_IN_ACCOUNT_B"
        },
        {
            "Sid": "AllowExportSnapshot",
            "Effect": "Allow",
            "Action": [
                "rds:DescribeDBSnapshots",
                "rds:DescribeDBSnapshotAttributes",
                "rds:ListTagsForResource",
                "rds:CopyDBSnapshot"
            ],
            "Resource": "arn:aws:rds:REGION:ACCOUNT_A_ID:snapshot:SNAPSHOT_ID"
        },
        {
            "Sid": "AllowS3BucketAccess",
            "Effect": "Allow",
            "Action": [
                "s3:PutObject"
            ],
            "Resource": "arn:aws:s3:::BUCKET_NAME/*"
        }
    ]
}

The policy in Account B then would look like:

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Sid": "AllowAssumeRoleAccountA",
            "Effect": "Allow",
            "Action": "sts:AssumeRole",
            "Resource": "arn:aws:iam::ACCOUNT_A_ID:role/ROLE_NAME_IN_ACCOUNT_A"
        },
        {
            "Sid": "AllowS3BucketAccess",
            "Effect": "Allow",
            "Action": [
                "s3:PutObject"
            ],
            "Resource": "arn:aws:s3:::BUCKET_NAME/*"
        }
    ]
}

Hope this helps.