Not only are they supposed to be there, I'm about to turn you into an uber-nerd who can tell the difference between James Webb Space Telescope pictures and Hubble Space Telescope pictures.  

So those 'lens flares' as you call them are technically defraction spikes and they work through very complicated optics that I don't care to understand, personally, and basically, those spikes are there because one, this is the hexagonal mirror and two, there are struts holding the secondary mirrors, so the light comes in here and then it hits this mirror, bounces off that mirror, and goes into this little detector here.

The hexagonal mirror gives us these six spikes and then one of the struts gives us this one.  The other two struts actually, their flare lines up inside of these spikes.  Now, these won't be as intense as they are in this image, this is way brighter than any star JWST is designed to image, but if there is a fairly bright object in the image, this pattern of spikes will tell you that it's a JWST image.  

Hubble, on the other hand, just has these four struts, and that means Hubble images have just four spikes.  Now you can read space pictures!