Ok....making a chute is the easy part....animating it is a tad harder...or rather its fiddly....##
In this scene Ive got
1,     Pic 1,...chute and ropes. all one mesh Called Chute     and a contoller mesh box Called Dragchute,which you cant see but I will show you how and why its there etc.... 2,    Pic 2,.....once created,your chute and ropes,move them to where they will be in place when deployed.
   Ive attached ropes to chute,I will show why next.
3,
    Pic 3,...When animating chute,best result is to scale the vertices to get the chute to correct size from packed to fully deplloyed.
   Pic3a
,........all I did was to scale the chute down to fit in the chute housing....if your fussy you can scale it to look like real chute deploying by scaling it in Y axis (Pic3a) then X and Z axes

   (Together )
animated by scaling down vertices....ensure controllers set to TCB Rotation TCB Scale and TCB Position.

4,
Pic 4,...I left space in animation slot,because we need create a parent box named It Dragchute....as this is what we will add as the chutes name in the data.ini  later.... (link the chute to this box
5,
before animating the chutes placement)
as we cant animate the chute again for movement,this box mesh gives us more scope to get the chute opening correctly.....so the chute opens smoothly...this box will be made tiny as we

dont want it seen..you will need to experiment where to place the parent box when you animate the moving of the chute in place....as in pic 4..
open box properties and set user defined so...for this parent box chute manipulator mesh...

AllowDecals = False
CastShadow = False
CatchShadow = False
UseFlatNormal = False

6,....with animation keyframe enabled,  move the scaled chute in proper position,and close keyframe....then move the keys so it looks smooth in animation timeline...

when you are happy the animation is smooth enough,you can then link the controller box to whatever mesh you want. Pic 6 finished item
hope this explains how to get the chute animated ok....
trial and error is really all it is to get it correct,move a little,test,move again test etc etc...
cheers