Hi & welcome to LQ. Sorry that your post didn't get any replies.
Did it get solved over the past month?
I'm not familiar with GUI, but I'll toss out a few ideas.
LQ is kinda adverse to Kali (for non-experts; search Titles & you'll see). But
it's probably not a Kali issue; the kernel + video drivers are same for all distros.
A couple typos: I think it might be haswell (other spellings return misleading search results)
I think you mean: my laptop screen started flickering; my TV, which I use as a second screen via hdmi, is fine (not: "...flickering on my tv...": I added punctuation)
More info/details (and any 'log' messages always!) might help: inxi -G
Here's a couple (wild-guess) things I found from web-searching:
https://forums.kali.org/showthread.p...t-dist-upgrade
This search returns a lot; maybe the results would suggest additional keywords (to narrow):
linux video|screen flickering "haswell"
I/we hope to hear back from you! Best wishes!