I just made my delta flyer, at what level can I get a ship where I can launch the delta flyer from? I am lieutenant commander 8

If you visit the transporter room from any ship interior you should have the option to switch to your shuttle/runabout/delta flyer.

f(t) is correct. Go to your interior in order to switch to your shuttle craft. I highly recommend writing down the where your bridge officers are assigned to on your ship's BOff stations. When you switch back to your ship you'll need to put them in their original stations in order for your shortcut tray to reset back to the way you had it.

I would also like to say that you can visit your shuttle's interior in order to switch back to your ship.

Thanks guys, awesome thanks again

You can also visit the ship selection officer at the major shipyards to switch between ship and shuttle as well. This was the only way till the recently added the shuttle interior and the capability to do it from your ship.