Chally,
The south entrance to Yellowstone is still closed. I am hopeful that it will open before you get there, but you really can't completely predict fire behavior.
If it is still closed, don't despair. From Jackson to Madison Junction (in Yellowstone) is about 3 hours, regardless of whether you go in Yellowstone's south or west entrance. If the south entrance is closed, head out of Jackson over Teton pass to US 20. Google Maps gives good instructions for this route.
Google says the trip is a half hour faster going through the south entrance. In my experience, it takes the same amount of time either way (and I have done both ways many times). The drive is beautiful either way.
Note that Madison Junction is about 16 miles north of the Old Faithful area. If there are no "buffalo jams" along the way, that makes it about a half hour drive from Madison Junction to Old Faithful.
Steve