Parachute/Glide

What I would do is have all your falling logic be placed in a different script or function IE:

 function ParachuteLogic()
 {
     if(parachuteIsOpen) //this is short hand for parachute == true
     {
 
     }
 
 }

Then within your update keep checking for that P button press so:

 function Update()
 {
     if(Input.GetKey(KeyCode.P))
     {
         parachuteIsOpen = true; 
     }
 }

This helps keep things seperated and extendable. Its now easier to add your jump into the mix to detect for that. So now we will update our update function.

 function Update()
 {
     if(Input.GetKey(KeyCode.P))
     {
         parachuteIsOpen = true; 
     }
 
     if(Input.GetKey(KeyCode.Space))
     {
         playerIsJumping = true; 
     }
 }

We can now take our same though process as keeping things compartimentalized and seperate and use that for our player jump. So in a new function we can do something like this:

 function Player()
 {
     if(playerIsJumping)
     {
         var timeSinceJump : int += Time.deltaTime; // you could us this as your timmer
     }
 }

You also said you didn't want to allow the user to activate the parachute if the user jumped so you can now simple do this in that update function:

 function Update()
 {
     if(Input.GetKey(KeyCode.P))
     {
         if(!playerIsJumping) // this is shorthand for playerIsJumping == false
         {
             parachuteIsOpen = true; 
         }
     }
 
     if(Input.GetKey(KeyCode.Space)) // space is a common jump button in games, but this can be remapped. 
     {
         playerIsJumping = true; 
     }
 
     Player(); // make sure anything that uses time is  included in your update function
 }

I think the majority of your problem is not viewing things as individual steps and breaking it down into those steps. Not sure exactly what your problem was, but I hope this answered your parachute opening while jumping problem. Let me know if you have any more questions or need anymore help!