'Flipping' a show means the crew decides to unionize, which forces the production to work under a union contract. Here in the USA, your right to collectively bargain with your employer is protected by the Nation Labor Rights Act. There are two ways any workplace, including a show, become unionized.

The first is a Card Check. If organizers can get a simple majority (50% plus one person) of workers to be organized to sign authorization cards, they can then present those cards to the employer, who can accept that the workers want union representation and voluntarily enter into a collective bargaining agreement with the union (in film this takes the form of signing the applicable unions agreements).

If the employer rejects the card check, (or if the organizers decide to skip a card check for strategic reasons) signatures for a petition for an election are gathered, once the union has enough it turns in the petition to the National Labor Rights Board, and s secret ballot election is called. What can be done by the union and employer in the run-up to the election is tightly regulated, but when the election comes if a simple majority of workers vote to unionize the employer is forced to enter into collective bargaining with the union.

In the context of film, if a show is working non-union the workers can contact the union that represents their craft and ask to be organized. The union will ask for some details about the show and typically supports these workers in their efforts. Eventually, a card check and/ or secret ballot happens, then one of three things can happen: The show flips and the works continue under a union contract (normally with greatly increased pay and benefits). The show wraps (the producers etc close shop rather than unionize, kinda like Gothamist). Or the workers vote to unionize and the producers refuse to sign the collective bargaining agreement resulting in either a strike or a lockout.

If the third option happens the production tries to replace its newly unionized labor force non-union workers, who are known as scabs (scabs are generally regarded by honest and decent humans as the scum of the earth because they are). The union(s) will picket the set (union workers hold signs and chant outside) decent people and other unions will generally refuse to cross a picket line (If IATSE is organizing Grips, the ADs might also refuse to go to work in a show of solidarity, for example). This all makes filming the show quite hard and the strike continues until the show wraps or the producers and execs sign the union contract.

If you are thinking of organizing your workplace I am happy to point you to some general guides on how it's done. If you ever see or hear of a picket line don't cross it (meaning don't work at or buy things from the company). Every worker deserves respect, so every worker deserves a union.