You probably can't do it.
What you *MIGHT* be able to do is to clone the <form> on the Nike site to your own site, making sure that the action= of the <form> still points to the Nike site. Then you could use your own JS code on your own site to fill in the <form> and submit it to the Nike site. More than likely, that won't work. And that's because, of course, to Nike you look like somebody trying to hack their site and submit bogus orders. So, like most modern sites, they will have all sorts of code in place to detect attempts to do this very thing. Just for example, and the most obvious thing to check and the easiest for even a beginner in server-side programming to implement: Whan any <form> is submitted (or any page is linked to another, for that matter), the receiving site can check something called the HTTP_REFERER, which tells it what site *AND PAGE* the <form> or other link came from. And if the REFERER is not what the site is expecting, it rejects the attempt.
SO... If you are truly a newbie, I'd say you are very very unlikely to succeed at this. And if you aren't a newbie, your changes of success are still pretty darned small.
An optimist sees the glass as half full.
A pessimist sees the glass as half empty.
A realist drinks it no matter how much there is.