I'm playing FF toys, my opponent is playing TT

On 5 I drop stretch, and then play a fantasticar on IW. In response he uses Harper's ability to stun Stretch.

First is this legal, and secondly, can I respond by throwing a flamethrower on stretch?

Yes, it's legal.

Recruitment is an effect like any other so you must pass priority to your opponent before it resolves and puts a character into play.

As for your response, if Flamethrower is already in play you may transfer it.

However, you may not recruit it as recruitment must happen on an empty chain.

Any time you recruit a character or equipment both players have a chance to play effects. This means that after you pass your opponent would have the chance to use Roy Harper's effect. However before Roy's effect resolves you would again have a chance to play your own effects like using a flamethrower or Stretch's transfer effect.

Finally though you cannot recruit characters or equipment except on an empty chain. So there would be no way to add a new piece of equipment onto the field until all effects resolve.