My FM transmitter never works, Why?
Forget building this on a breadboard.  The oscillator can't work on a breadboard.
Breadboards have capacitance between the pin rows that's about the size of the capacitors in the oscillator.
Breadboard pin rows have about the same inductance as the coil in your oscillator.
These inductances and capacitances are not some part you could remove from the breadboard.  They are a side effect of the way breadboards are built.
Besides all that, the wires used to connect things on breadboards are usually long enough that they have inductances that are as high, or higher than, the inductors in the oscillator.
If your oscillator could work, you wouldn't need the 741.  The 741 is there in the original circuit to amplify the (very weak) microphone signal to a level high enough to modulate the frequency of the oscillator.  The output of your phone's headphone jack is already high enough to do that.

You'll need to build this on a piece of perf board, keeping the connections as short as possible.
You'll have to solder the connections.
Coils made of wire with thick insulation won't work.  The insulation between the windings will act like a capacitor in parallel with the inductor. You need thin wire with enamel insulation.  Random wire salvaged from whatever is at hand won't work.
If you should by chance get that circuit to work, you will find it to be very finicky and touchy.  The transmit frequency will change depending how close you are to it, how close other things are to it, how hot or cold it is, whether you are looking at it cross eyed (or not) or for no discernible reason at all.
The circuit you have found is the simplest circuit that can be used to demonstrate the concept of an FM transmitter.  It is not a practical circuit at all.