Have you tried to delete and reinstall app?
Are you able to set up with Ethernet for the PS4?
I doubt a picture flickering / flashing problem is related to your NOW Broadband service.
Does the flickering or picture flashing occur on other Apps on your PS4 ?
Is your PS4 connected directly into your television HDMI port or are you using an AV Receiver or HDMI switching Hub ?
Can you test your PS4 on a different television in your home with a different HDMI cable.
If the flickering is happening when watching NOW Sports rather on the main App screen, then check that the PS4 Display settings is set to 50hz.
Because the other Apps a running fine, then i doubt it's your Broadband service.
It does sound that the NOW App is corrupted or conflicting somehow with your PS4 setup.
Have you tried going into the PS4 Display settings and see if there is an option for 50hz output ?
Does the flickering happen on both the NOW App main screen and when watching NOW content or only when watching something on NOW, but the main App UI screen is flicker free ?
Can you try the other suggestions that i posted ?
I don't own a PlayStation, but if it was me i would try Googling on the internet something like "Picture Flickering on PS4" (even if it doesn't effect other Apps).
I am out of ideas because i don't own a PS4 or any game console when watching NOW.
The NOW App is sensitive when using HDMI with an external device more than other Apps.
Can you try a different HDMI cable with PS4 plugged directly into your television.
Would you have another television around the home just to temporary test the PS4 out with the NOW App.
I am also assuming you are not using a VPN with your PS4 ?
Hopefully other forum members will come to your rescue on what needs to be done to fix it.