Calling Web API from MVC generic way of approach

I agree as some others have said that in this case, having a layer between Angular and your API is simply bloat / overhead unless there are specific reasons for the extra abstraction. I understand that you are late in the project development so my review will reflect that but as an aside I have to point out that your management should have a COMPLETE understanding of the technical debt incurred by any potential "Escalation of Commitment" mistakes made by them. Especially considering Web API will eventually be deprecated: https://blog.tonysneed.com/2016/01/06/wcf-is-dead-long-live-mvc-6/

That being said, your code for the most part is fine but I would suggest a couple of architectural changes.

1. Keep your controllers thin

Controllers only responsibility should be to retrieve data and pass that data to the view. In this case, your view is JSON, so your controller should ONLY make a cal to get data.

As the code currently is it is also more difficult to test than it needs to be.

2. Encapsulate methods

As you have pointed out, you are winding up with a lot of duplicate code. I would suggest solving both problems by introducing another layer of indirection.

Example Code

Controller Code

public class MyController : Controller {
    private IApiClient _apiClient;

    public MyController() : this(new WebApiClient()) {
        // Poor-man's DI in case you don't have an IoC container.
        // If you do, do not include this constructor
    }

    public MyController(IApiClient apiClient) : base() {
        this._apiClient = apiClient; // assign injected dependency
        // This injected dependency streamlines your testing process
        // because the results are more easily mocked than direct access
        // to the HttpContext as was done in the actions before
    }

    public async Task<ActionResult> GetStates() {
        string relativePath = "api/Admin/GetStates";
        return await this.ApiGet(relativePath);
    }

    public async Task<ActionResult> GetClients() {
        string relativePath = "api/Admin/GetClients";
        return await this.ApiGet(relativePath);
    }

    public async Task<ActionResult> Roles() {
        string relativePath = "api/Roles";
        return await this.ApiGet(relativePath);
    }

    protected async Task<ActionResult> ApiGet(string relativePath) {
        ApiResponse response = await this.ApiClient.GetAsync(relativePath);
        ActionResult result = response.IsSuccessful ? new ContentResult { Content = response.Data, ContentType = "application/json" } as ActionResult : new JsonResult();
        return result;
    }

    protected IApiClient ApiClient {
        get {
            return this._apiClient;
        }
    }
}

The ApiResponse class

[Serializable]
public class ApiResponse {
    private bool _successful;
    private string _data;

    public ApiResponse() {
        this._data = string.Empty;
        this._successful = false;
    }

    public string Data {
        get {
            return this._data;
        } set {
            this._data = value;
        }
    }

    public bool IsSuccessful {
        get {
            return this._successful;
        } set {
            this._successful = value;
        }
    }
}

The IApiClient and WebApiClient types

public interface IApiClient {
    Task<ApiResponse> GetAsync(string relativePath);
}

public class WebApiClient : IApiClient {
    private System.Net.Http.HttpClient _httpClient;

    public WebApiClient() {
    }

    protected Uri BuildCompleteUri(string relativePath) {
        // Using a URI will help us to validate the URL before making an invalid call.
        Uri returnUri = new Uri(VirtualPathUtility.Combine(this.Client.BaseAddress.ToString(), relativePath));

        return returnUri;
    }

    public async Task<ApiResponse> GetAsync(string relativePath) {
        Uri completeUri = this.BuildCompleteUri(relativePath);
        ApiResponse response = new ApiResponse();
        HttpResponseMessage apiResponse = await this.Client.GetAsync(completeUri);
        if (apiResponse.IsSuccessStatusCode) {
            string responseData = apiResponse.Content.ReadAsStringAsync().Result;
            if (!string.IsNullOrWhiteSpace(responseData)) {
                response.IsSuccessful = true;
                response.Data = responseData;
            }
        } else {
            // TODO: Log Errors
        }

        return response;
    }

    public HttpClient Client {
        get {
            if (this._httpClient == null) {
                this._httpClient = HttpContext.Current.Items["httpclient"] as HttpClient;
            }

            return this._httpClient;
        }
    }
}

The above code structure keeps your controllers thin, reduces code duplication, allows for extension points if you need to add more information of your own to the ApiResponse type, and dramatically simplifies your unit testing process because the IApiClient type is easily mocked.

You could even take it a step further and use the DI container to register a factory method that injects the HttpClient instance into the WebApiClient type, which would also simplify the testing process of the WebApiClient.

I also renamed your controller actions so they are consistent with the API method they invoke.