If you’re not going to elevate to avoid the lights, you’re going to have flare. As others said, make it part of the overall image. And the poster who suggested some front light on your subject was bang-on. Right now the cyclist is very dark.
Oh, and it’s the spiking (vertical smear) that really mucks up the picture, not the flare. Flares I can live with as a compositional element. Spikes, not so much.