Wasn't able to discern this from the rules reference:

Can we play conflict characters during ANY action window? Quite relevant now that we know the Fate phase and Regroup phase both have action windows.

Yes - you can play a conflict character during any action window. This means you can drop one after conflicts for the Imperial Favor challenge if you need.

1 minute ago, shosuko said:

Yes - you can play a conflict character during any action window. This means you can drop one after conflicts for the Imperial Favor challenge if you need.

Not quite. You cannot play them during your action opportunity in the Dynasty Phase. Otherwise, yes.

I mean can you play one when it is specifically not the conflict phase or dynasty phase.

4 minutes ago, kiramode said:

I mean can you play one when it is specifically not the conflict phase or dynasty phase.

If you want to, yes. Remember there's no "stack" in L5R, so you can't play a conflict character "in response" to something, though.