Luminous flux is the measurement of visible light emitted by a radiating source, as we perceive it. Expressed in lumens but with one important difference between the lumens emitted by the radiating source and the luminous flux that we perceive from it - the difference is that lumens define the total energy within the visible spectrum that the source, such as a light bulb, is giving off. To derive these measurements, we start with radiant flux, which all of the electromagnetic radiation that the source is emitting. Lumens are the measurement of that portion of the total radiation that is visible to us. To pick some examples, the source might be radiating some energy in wavelengths that are too long for us to see, such as radio waves, or some that are too short, such as X-rays, or both. Those are not counted when we calculate the lumens the source is emitting.
Then, to derive the luminous flux, the visible lumens when analyzed for their wavelengths and the different portions of the spectrum and weighted to account for the different ways our eyes react to them. Picking some examples again, if two light sources are emitting the same amount of lumens but one of them is giving off mostly blue light and the other is giving off mostly red light, the one emitting the blue light will have more luminous flux than the one putting out the red light. That is because our pupils dilate and we take in more light when the available light is very blue, and they contract, so that we take in less light, when the light is red.
Lumens and luminous flux are closely related but they are not the same.