Chicago United Center to Midway Airport

Getting a taxi when 1,000 other people are trying to do the same thing at the same location is practically impossible. I doubt you could get an Uber either, at least not without paying an insane surge price.

Barring having a really good friend to pick you up and drive you, your best bet here really is public transit.

The 19 and 20 buses will stop on Madison in front of the United Center after the game, but these also will be crowded and you may still have to wait a while.

To really beat the crowds here, I would walk a few blocks to the nearest L station (~ 10 mins). Go east toward the lake down Madison to Ashland, turn left, and pick up the green or pink line from Ashland station to the loop (~ 5 mins). Transfer at Clark/Lake or Adams/Wabash to the orange line all the way to Midway (~ 27 mins). At the time you should be getting out of the game (it starts at 2pm so I figure you should be leaving around 5pm), trains are still running every 10-12 minutes, so you should have little difficulty getting to Midway by 6pm.

Another option is the airport shuttle. You can book this in advance and ask them to pick you up somewhere nearby. But with the expected traffic congestion, this may not save you any time, or it might even cost you time.