"using" disposes (destroys) an object when it leaves the using context, so your HttpClient is not usable outside of the GetClient method. Remove the "using"
public static HttpClient GetClient(string url)
{
HttpClient client = new HttpClient();
client.BaseAddress = new Uri(url);
client.DefaultRequestHeaders.Accept.Clear();
client.DefaultRequestHeaders.Accept.Add(new System.Net.Http.Headers.MediaTypeWithQualityHeaderValue("application/json"));
return client;
}