What do your dragons look like? This question could derail this entire answer, but given the description you do have, I think this could fit.
Your dragons have the equivalent leg strength of the grasshopper (or flea, or pick you favorite jumping insect)1.
The dragon has the ability to quickly wrap it's wings around it tightly, creating a near perfectly aerodynamic form - twisting it's body roughly 720o each time it takes off2.
So your dragons simply jump to take off silently. The turning forces air off the ground to follow the dragon up and fill the vaccum left more smoothly. So there's still some leaves rustling, and some air movement for 100ft along the ground3
See notes below4
1Yes, whatever bio-fibers make up their legs will have to be something that doesn't actually exist from a physics/reality standpoint - at least that we know of or can dream of so far.
2 At full strength this does indeed create a sonic boom, but if attempting to, the dragon knows the correct strength to use to get itself just high enough it's wing noise isn't audible to a human, without creating said sonic boom. This is pure speculation, it could easily not be possible for a creature of this size to leave the ground with enough speed to get high enough without creating a sonic boom. This would depend on gravity, air density, etc. Not sure if we're assuming all physics are identical to ours?
3 Estimated, hopefully obviously.
4 Yes, yes I did just find the superscript/subscript tags for SE