Not quite - you will not get Kris Flyer miles, you will get M&M miles for flying SQ. The miles M&M gives for any given SQ flight may or may not be the same as SQ would give to a Kris Flyer member.

You can use Kris Flyer miles ( in a Kris Flyer account) to book a LH/LX flight.
You can use M&M miles, in an M&M account, to book a SQ flight.