Inside foreach binding the binding context is item of collection, not the root view model. To get access to parent context in foreach binding use $parent, like this:
<div data-bind="foreach: MyFmnu">
<!-- ko if: key === 'ASM' -->
<input type="checkbox" value="ASM" class="styled"
name="fldMenuCheck_Acc1" id="fldMenuCheck_Acc1"
style="width:10%;"/>
<!-- /ko -->
<div data-bind="foreach: $parent.MyFmnu1">
<!-- ko if: key === 'ASMS' -->
<input type="checkbox" value="ASMS" class="styled"
name="fldMenuCheck_Acc12" id="fldMenuCheck_Acc12"
style="width:10%;"/>
<!-- /ko -->
</div>
</div>
more info here: http://knockoutjs.com/documentation/binding-context.html