While it's fairly obvious how to replace the battery in a regular Mz3/MS3 keyless entry remote (use a coin to split the case open, replace battery, snap case closed), it's a little less obvious for the flip key. Here's how to take the flip key apart to replace the remote battery:
Replacement CR1620 button battery
First, we need to separate the key portion from the remote portion. Flip the key blade open, then look in the slot where they key blade is stored when it's closed. Note the little tab in this slot in the picture below:
This part is a little tricky. Hold the flip key in one hand, then push the tab in the picture above with the screwdriver in your other hand. While holding the tab in, pull the key portion away from the remote portion. Some people might find it easier to hold both the remote portion and the screwdriver in one hand, then use the other hand to pull the key portion off.
If you're successful, you'll end up with this:
On the remote portion, note the little slot right below the "VISTEON" writing on the now-exposed part of the remote portion (in the compartment where the "tab" of the key portion goes into). Stick your screwdriver in this slot, then tilt the screwdriver so it's parallel with the face of the remote:
You should now have the case cracked open a bit. Grab the two halves and unfold them as if the metal keyring part on the bottom is a hinge. The two halves should come completely apart:
The remote PCB stays attached to the "top" (button side) half of the remote; the battery sits in a compartment in the "bottom" half, and supplies current to the PCB through a couple of metal tabs that make contact when the remote is snapped shut.
To remove the old battery, press on it as indicated here, and the battery will flip up so you can grab it and pull it out:
Insert the new battery into the compartment, making sure the positive (+) side is facing downward.
Snap the two halves of the remote portion back together.
Snap the key portion back into the remote portion.
You're all done!