Just to confirm what you have:
This is a ball lock beer QD with a flare fitting
This is a ball lock beer QD with a barb fitting
The former - at least the one shown - has an integrated gasket at the tip of the male flare. It will seal on its own when screwed tightly into one of these swivel nut/barb fittings
If you happen to have a flared QD that doesn't have that little gasket/o-ring at the tip (I've never seen one, fwiw) you need to buy some of these. You insert one (bevel side away from the QD) into the swivel nut before screwing in the QD.
Now, backing up, if your QDs are actually the barbed type, they are meant to go directly into tubing with a hose clamp keeping things tight. There's no place to use any tape in that case.
If you could let us know what style QD you actually have we'll all be in sync...