Blue Aprons affiliate program: Is on Impact Radius: https://www.blueapron.com/pages/affiliates
Peleton: Looks like they had a referral program, but removed it (info here: https://www.reddit.com/r/pelotoncycle/comments/71b2k1/peloton_has_banned_referral_code_sharing_and_how/)
Leesa: On Impact - https://www.leesa.com/pages/affiliates
Boll & Branch: Looks like they were on ShareASale but no longer (although Viglink signup is still there: https://www.viglink.com/merchants/53747/boll-and-branch-affiliate-program)
As you can see - there is not one central network that these types of merchants run their affiliate program through. I would decide who you want to work with and then go the route of seeking their affiliate program out. If that is too manual (i.e. if you are talking about 100's of merchants for which you don't want to signup for each) and don't mind parting with a small amount of the total offered commission - you can signup for skimlinks or viglinks and auto monetize your links that way.
Hope it helps!
I'm a Youtuber with over 80,000 subscribers and an Affiliate Marketer and Influence Marketer. I've worked with a number of brands over the years.
In terms of the best platform for connecting with these brands, there are platforms like GrapeVine Logic, FameBit, Social Blue Book, and Intellifluencer which act as kind of a middle man or escrow service between brands and influencers.
These platforms are a great place to begin searching for brands, but oftentimes you may find the specific brands you want to work with aren't listed on these platforms.
One thing I've noticed as of recently is many if not most companies seem to have a position or even an entire department of their marketing team who's devoted to finding and working with influencers and managing collaboration efforts.
If you're not seeing the brands you'd like to work with reach out to them directly either via social media or an e-mail listed on their site.
Are you a Youtuber or Blogger?