Materials Needed:
1x Rocket (from the weapons tab).
1x Detacher.
1x Fuselage (this is just for connections and looks).

To start off, select the rocket, open its settings, set fin mode to "None", and activation group to "All" (not strictly required, but I would recommend it). With the selected rocket, open the XML editor, add a text field, set the name to "burnTimer" and set the value to however many seconds you want it to burn for. Add another text field, name it "selfDestructTimer" and set the value to "9999999999" (so that the rocket doesn't immediately explode after it burns out). Connect the rocket to the fuselage. If you're really fancy, make the fuselage smaller, and fit the rocket inside of it to make a rocket tube, which can be saved as a subassembly to make bigger rocket engines from multiple tubes. Then, connect the detacher to the fuselage (preferably the non-detaching end). Next, open the connection editor add a connection between the rocket and the detaching end of the detacher. The rocket should be connected to the detacher and the fuselage. Now all you have to do is press a button, and you're off!

The rocket engines (like in real life) work better at higher altitudes. If you use the rocket tube method I listed above, you can go over Mach 1 (depending on the altitude and the aircraft). It is even possible to get into space with enough of these (I have done this, I can confirm it is possible to surpass 1,000,000ft with 9 rocket tubes).

On a side note, even after the rocket burns out, the exhaust trail will keep going, this does not mean the engine is still burning.

Thoughts or suggestions? Let me know!