I have no reputation or contacts. I'd be happy to offer my services for free to gain market recognition and reputation, but how would I go about getting companies as large as Kogan and Ikea to even accept my service?
My advice would be to read The Four Steps to the Epiphany by Steve Blank and think hard about his approach.
Beyond that, how do you contact people who work at Kogan and Ikea? Two obvious thoughts come to mind:
1. Go to the places they go and meet them there. There are undoubtedly annual conferences, expos, trade shows, etc. that cater to that industry. People from the companies you want to meet will be there, either presenting, or observing, or both. Go to those events and talk to people.
2. Go on LinkedIn and search for employees of those companies. Ideally you'll find at least a few who you either already know, or at least have a mutual connection with. Reach out to the ones you know, or if you only have a mutual, reach out to your mutual and see if they can connect you to the person you want to talk to.
Also, a variation on (2) that I personally like... still go on LinkedIn, but search for former employees of the target company. Reach out to them cold (unless you just happen to have a mutual with them) and explain politely that you're working on something that might be of interest to their former employer $WHOEVER, and that you'd like to ask them some questions to help you get oriented about the industry, that company, etc. The thing about this is, people who work for a company will tend to be somewhat defensive if you reach out to them directly, because right from the jump you come off as a sales-person who is trying to sell something to them / their current company. But if you present as being interested in their former employer, there is less reason for them to be guarded / defensive, but this still appeals to their need to feel valuable / knowledgeable / etc.
No, it won't work every time. But it works quite often in my experience. So meet with this former employee, find out if they think your idea has merit, and why or why not, yadda, yadda, yadda. And, assuming they left $WHOEVER on good terms, there is a good chance that they can be the person to arrange a warm introduction to somebody at your target company.
All of that said, I still advocate reading The Four Steps to the Epiphany (and maybe also The Mom Test) before reaching out to these folks.