What is the maximum side slip angle that can be achieved by a F-16?
Knife-edge flight is an aerobatic maneuver where an airplane is flying on its side for an extended period of time without ascending or descending.


Notice it says aerobatic, i.e. for show. There is no point doing it on a mission (or otherwise) in an F-16.

Spoiler: it can't be flown in an F-16.


  The flight control computer (FLCC) of the F-16 further incorporates limiters governing movement in the three main axes based on attitude, airspeed and angle of attack (AOA); these prevent control surfaces from inducing instability such as slips or skids, or a high AOA inducing a stall. The limiters also prevent maneuvers that would exert more than a 9 g load.
  
  — Wikipedia


One source mentions 10° of beta (sideslip angle) as an extreme and unusual for an F-16.


  Departure from controlled flight / Rudder input
  
  The Aileron Rudder Interconnect (ARI) automatically provides rudder input according to pilot roll input
  to reduce sideslip during turns. Pilot induced rudder does not improve turn performance but increases
  departure possibility.
  
  Yaw FLCS
  
  Since the rudder is mostly controlled in flight by the FLCS through the ARI (Aileron Rudder
  Interconnect) the pilot should in theory have no need to use the rudder in flight. To prevent pilot
  induced rudder movement which can create adverse effects the FLCS automatically limits its use.
  Rudder authority is reduced as a function of AOA, roll rate and CAT config to prevent departure from
  controlled flight.
  
  — BMS manual


Note: Crosswind crabbed flight is not a sideslip. The flight is coordinated (ball centered). Since the wind pushes the plane off track, the pilot corrects by pointing into the wind, that's all.

Just as tailwind or headwind has no effect on the flight dynamics, so is the crosswind. A plane flies inside a mass of air, if the mass of air happens to be moving, it only affects the navigation (where the plane is actually going, and how fast/slow).