Can I use the Khalim's Will flail after completing the Khalim's Will quest?

Yes, but not with the character that completed the quest.

The following is based on in-game experience and direct testing:

Prior to smashing the Compelling orb, you can transfer one or more flails to other characters (i.e. 'mule' them). After the mule has left the game with the extra flails, smash the orb with one of the flails remaining in the game. Once the orb is smashed, all party members will complete the quest.

The flails that were muled away will not disappear, and can be given to other characters who have not yet completed the Khalim's Will quest. Since the flail has no requirements whatsoever - level, strength, or otherwise - it makes an amazing weapon for level one characters.

Or, you can use one of these completed flails to skip the tedious part of Act III. You can go directly to Travincal, kill the council, and use a flail completed in another game to smash the orb. You will, of course, lose the flail.

But, a character who has completed the Khalim's Will quest in a particular difficulty level will be unable to pick up a Khalim's Will flail in that same difficulty level. Attempting to do so will result in the character saying things like "I can't do that" and "Impossible".