I'll be honest, F1's fashion Thursday posts were not my favorite thing on F1 Reddit. I'd prefer a new /c/f1fashion community than to start seeing posts of everyone's outfits here. But in the spirit of growing the sub, even if not in my favorite direction... I suspect you'll need to gather images from many sources including:

• Subscribe to a bunch of driver Instagrams. Lewis's insta has his outfit for today.
• Subscribe to a bunch of F1 photog Instagrams and twitters.
• Get RSS feeds or just manually check F1 photog websites. Like https://www.kymillman.com/photography/formula-1/ has an "images from the track" section that seems to be updated near realtime. The day-1 British GP link has images from today, including a view of Lewis's outfit (though Kym's happens to be a worse angle than Lewis's today... you're going to have to check multiple sources to see who got the good shot in any given day).

Good luck, and be ready to follow a decent number of non-federated socials to find good images each week.