I think this feature is not provided by the AWS SDK iOS since there is an open issue on GitHub which was closed unanswered. [1]
Instead, you can query the service directly using the service's so called IAM Query API [2].
AWS states that:
AWS provides SDKs that consist of libraries and sample code for various programming languages and platforms (Java, Ruby, .NET, iOS, Android, etc.). The SDKs provide a convenient way to create programmatic access to IAM and AWS. For example, the SDKs take care of tasks such as cryptographically signing requests (see below), managing errors, and retrying requests automatically. For information about the AWS SDKs, including how to download and install them, see the Tools for Amazon Web Services page.
Unfortunately the iOS SDK is not officially supported by the IAM service. That is why the IAM service endpoints are not included in the iOS SDK. You could try to open another feature request on GitHub though...
If you decide to implement the HTTP client and proper request signing manually, you can use the IAM commands which you mentioned above (in AWS terms called "Actions"), e.g. the ListUserPolicies action [3].
Suggestion for Improvement
I could then check the Action field in the IAM policy if it allows permission like "s3:GetObject" or "s3:" and resource field contains the value as "arn:aws:s3:::examplebucket/" or "*". If both applicable then IAM user has permission to the S3 "examplebucket".
If you want an approach which is more robust, I would suggest to use the IAM Policy Simulator API. [4]
References
[1] https://github.com/aws-amplify/aws-sdk-ios/issues/496
[2] https://docs.aws.amazon.com/IAM/latest/APIReference/Welcome.html
[3] https://docs.aws.amazon.com/IAM/latest/APIReference/API_ListUserPolicies.html
[4] https://docs.aws.amazon.com/IAM/latest/UserGuide/access_policies_testing-policies.html#policies-simulator-using-api