I just tried below piece of code and it works perfectly , executed in local C#.net console application - it should work in the Function App environment also. Please try !!
Only difference is , I am just looping through the blobs. I know it can be done in a better way !
static void DownloadBlobToStream()
{
string connectionString = "DefaultEndpointsProtocol=https;AccountName=straccount;AccountKey=key;EndpointSuffix=core.windows.net";
string strContainerName = "roleassignments";
string blobPrefix = "test1.csv";
var blobServiceClient = new BlobServiceClient(connectionString);
var blobContainerClient = blobServiceClient.GetBlobContainerClient(strContainerName);
foreach (BlobItem blobItem in blobContainerClient.GetBlobs(prefix: blobPrefix))
{
BlobClient blobClient = blobContainerClient.GetBlobClient(blobItem.Name);
MemoryStream memoryStream = new MemoryStream();
BlobDownloadInfo blobDownloadInfo = blobClient.Download();
blobDownloadInfo.Content.CopyTo(memoryStream);
byte[] blobData = memoryStream.ToArray();
File.WriteAllBytes(@"c:\shiva\test2.csv", blobData);
}
}