Are self-grounding outlets appropriate for use in metal boxes with BX cable?
If the BX is properly installed, the cable's metal jacket should provide a ground path. BX should always be connected into metal boxes with the appropriate clamps so that the box itself is grounded. You can test for this using a voltage tester - the box should test at 120V to hot and 0V to neutral.

If that's the case, a self-grounding outlet receptacle installed in the box will be grounded. The ground terminal on the receptacle is connected to the box mounting hardware, so you're just having the box provide the ground path instead, and connecting it via the existing mounting hardware. Note that this method of grounding (relying on the BX jacket) is no longer code compliant, but it is functional and safe as long as there is a reliable grounding path.

If the jacket is not properly grounded, you can use a GFI to provide some ground fault protection. You can also run a new ground conductor in some cases.