Open Forum

An out-of-the-can gloss finish (gloss paint or a urethane topcoat) should not present a problem with slipping if the actors wear rubber soles or something reasonably soft. Water on the floor, of course, would be a problem.

The bigger issue is light bouncing off the floor and onto somewhere it's not wanted, like the eyes of the audience, aka glare. I would ask the director why he or she wants gloss paint, and what color it is, and go from there.

Painting your stage floor has longer-term consequences for keeping it a good working floor.  If you paint it with a gloss paint, then you will have to repaint it after the show to return it to the preferred matte black finish that is useful for everything else.  If this is just for a few scenes, or even a whole play, I suggest that you consider purchasing (or possibly renting) some high-gloss Harlequin stage flooring surface that can be rolled-out and secured, then removed when you are finished with the show.  This provides a more predictable dance surface with regard to friction, and a nice shiny surface for the desired visual effect.  As mentioned by others, be sure the Director fully understands the challenges that a shiny floor presents for lighting and the usually undesirable reflections this can create from the stage lighting.  By having a glossy area that just covers the necessary space you minimize the undesirable reflection zones.

I would make up some test "swatches".  Say on 4 x 4 sheets of Masonite or the back of old plywood, etc... to see if you can get the desired finish before painting the entire floor.

Glaze as a top coat can give a pretty glossy finish, for example.  

I would also recommend not painting the stage floor directly, rather work with a ground cloth or a Masonite floor or other surface as Eric recommends.

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Michael Johnson
Trinity NC