Flipping a nut around is not a good idea. On a well cut nut, the slots have a bit of an angle on their bottoms - the string goes from flat (parallel to the fretboard) to a down angle when headed towards the tuner. A well cut nut will have the bottom of the string slots cut at an intermediate angle - which gives you a gentler transition at each end of the nut slot, and the string "rides" on the bottom of that slot.
If you flip a nut, the bottom of the nut slot has an angle going the wrong way - the string will be "perched" on a ridge at the back end of the nut - all the force is on one point, and the string is now vibrating not from the front of the nut, but from the back - intonation wise that's not right, and it's likely to buzz in the slot. Having all the force on that point, the string is also likely to get hung up, making tuning stability a problem.
Nuts are seemingly simple, until you get into the details, when you learn they aren't really as simple as they seem.
Get a new nut and have it cut properly.