You need to just take care of setting the name of the checkboxes properly and you should be able to read the values in the post.
You can try something like below and it should have values posted in the controller action
<tbody>
@for(int i=0; i < handbook.Data.EmpDoc.Count; i++)
{
<tr style="text-align:center;">
<td>
<input type="checkbox" name="chk(@handbook.Data.EmpDoc[i].Filename)" />
</td>
<td>@handbook.Data.EmpDoc[i].Filename</td>
<td class="text-nowrap">@Html.ActionLink("Download", "DownloadFile", new { fileName = handbook.Data.EmpDoc[i].Filename, id = handbook.Data.EmpDoc[i].EmployeeId })</td>
</tr>
}
</tbody>