As much as possible. They don't climb and hang and chew like parrots, so in my opinion they need a lot of fly-time for enrichment as well as physical health. A caged pigeon might just sit on the perch and not get any exercise or fun in. How much room do they have in the cage? You should make sure that they have the room to stretch their wings fully and flap them, while inside. That often means less perches and toys. Space is the most important thing for a pigeon I think. So it all depends on your specific situation, but they should have at least an hour or more to play and fly out of the cage but on normal days I would aim for more than this.
My pidge has free fly, free roam all day, in the house,,that's the way its always been, but, I'm sure not alot would tolerate that, I would let her have few hours out of cage to fly, forage,,she will.learn where her cage/ home is..I tell Snowpea to go home and she flys to her cage..