For a Monk, Martial Arts and Unarmed strike lets you use any body part as a weapon, thus you can kick instead of punch.
I would allow this and the following is how I see it.
The orc expends 5 ft movement to make a spin/discus style throw. You convert your flight into a flying/jump kick and strike the target in the chest/head; using your legs to absorb impact and convert momentum into added damage. You possibly knock the target prone and land on your feet in front of the target.
The orc rolls to hit using STR bonus; 20 Ft normal, 40 FT long range. A failure means you land in a random square next to the target. If that square is occupied by an enemy, you may switch target to that enemy and proceed as if the roll was a success. If the orc rolls a natural 20, then you get +2 on your Athletics(DEX) check.
You roll an Athleltics(DEX) check to see if you successfully convert your flight into a kick. A fail means you take 1d4 impact damage. If the orc succeeded in his attack roll, the target also takes 1d4 damage. If the throw is 20 ft or less add the orc's STR bonus to the damage. If you roll a natural 20 on your check, consider your attack to be a critical hit (double damage).
If both rolls succeed, then you roll normal damage for unarmed strike (1d4+DEX or STR). If the throw is 20 Ft or less, add the orc's STR bonus to damage and the target needs to make a STR save or be knocked prone. You can add Ki Empowered Strike or Stunning strike to the attack for the cost of 1 Ki.
Note: A flying kick only allows one hit if you wish to land on your feet, so Flurry of Blows cannot be added to the attack.
Since you are making an attack outside your turn, I'd rule that the orc has used an action, and you have used a reaction.