In addition to Willeke's answer:
You can take the Heathrow Express to Paddington. This explains getting to Heathrow from King's Cross but you'll be able to apply it in reverse:
For the fastest route from Kings Cross to Heathrow simply take the underground (on either the Hammersmith and City line or the Circle line) directly to London Paddington. After your arrival, follow the signs and take the Heathrow Express from London Paddington straight to the airport.
The Express is £37 takes roughly 15 mins and you'll need to pay from Paddington to King's Cross.
I always assume disembarking a plane takes 20-30mins, customs 30mins, getting around the airport (it's huge! look up the floor plan), travel by/locating the train/underground, entering security again, etc... So overestimating time, it leaves less than 1 hr to view the platform/take a picture/shop.
I'd like to note by experience that the wait for a photo at King's Cross (trolly and House scarf) can be minimum 45 mins. The shop is cute and you'll be able to pick up some great souvenirs but isn't as diverse as the studio. Edit: The Harry Potter Platform 9 3/4 website has more information: You can purchase a VIP pass to quickly bypass the long line. It's free to take your own pictures but you have to pay for a professional print. Found on the FAQ:
Do I have to pay to take my own photographs at the trolley?
You do not have to pay for your own photographs at the trolley. You can however purchase your professional photo in store should you wish to.
If you're able to go to Terminal 5, you can visit the Harry Potter shop there. Not the same as a photo entering Platform 9 3/4 but if you're strapped for time, it's not a bad alternative.