[Note Edge Accessories] ccisn:
Thank you to the OP for this mod. I can verify this works great. I bought the original Samsung S Charger Cover from eBay. EP-CN915I. I think I ended up getting a Korean model of this back. Regardless it works great. I wish I had read this post before doing the mod because I too ended up with the Style clock quirk mentioned by Massam99 and took a bit of time to figure out how to set it back when the answer was right here all along.

I too can verify this workaround by Massam99 works.

Go to the Edge Screen settings and you will notice that the "Style clock on edge screen" settings are missing.

Stay on Edge Screen settings

Close the cover

Flip the phone so the edge bar is displaying horizontally

Open the case while edge bar is displaying horizontally

The Style clock on edge screen settings will be available (You can now orient the phone back to portrait)

Click on the settings and set to your liking

Once you go back you will notice the "Style clock on edge screen" is gone again. However the settings stick. They stick after powering off and restarting. I too have to keep doing this if I need to change the settings, but in reality I only needed to set it once. I don't change this setting much so for me I only needed to set it once. However in testing doing the above works every time. At first I thought it may have been an alignment issue with the pins and kept messing around making minor adjustments, but was not able to get the settings to come up as they did before the Qi modification.

I didn't have to modify anything on the flip cover other than carefully removing the 3 pin connector. Its glued on so it seems if you do not damage it during removal, you can just glue it back on to restore your flip case to factory condition.

Removing the guts from the original Qi back was pretty straightforward. Using a sharp thin knife I pried the corners up and then using a dull thin flathead screwdriver pried the backing apart. Once the back comes off as in the pictures, I just carefully removed the charging components using a guitar pick from a case opening toolkit. You can probably really use anything, even a screwdriver, but you might scratch some of the conductors if you don't use something plastic. Seems like a credit card might work as well. Once I removed the charging components I just used electrical tape to secure the components to the flip case. After that, other than the minor Style clock quirk, everything works great!

As a note on snapping the phone into the flip cover. The resistance seems to be a bit more than without the mod, but its probably because its a tighter fit now. Regardless the phone should snap in flush as it did without the mod. I don't have any extra bumps or bulgy spots. Once its snapped in it should fit as it did without the mod. If it doesn't, you probably need to realign the charging components so the phone can snap in correctly.

Thanks to ojcool and Massam99 for posting these helpful posts. I'm glad this had been tested. Its disappointing that Samsung doesn't have a Qi flip case. But now we can make them ourselves! The only con is that its kind a pricey case in the end. That all goes away with the satisfaction of doing this mod successfully, and the coolness factor it adds to now have something that cannot be purchased.