Submitting form and pass data to controller method of type FileStreamResult

When in doubt, follow MVC conventions.

Create a viewModel if you haven’t already that contains a property for JobID

public class Model
{
     public string JobId {get; set;}
     public IEnumerable<MyCurrentModel> myCurrentModel { get; set; }
     //...any other properties you may need
}

Strongly type your view

@model Fully.Qualified.Path.To.Model

Add a hidden field for JobId to the form

using (@Html.BeginForm("myMethod", "Home", FormMethod.Post))
{   
    //...    
    @Html.HiddenFor(m => m.JobId)
}

And accept the model as the parameter in your controller action:

[HttpPost]
public FileStreamResult myMethod(Model model)
{
    sting str = model.JobId;
}