Please point out as many holes and problems in my plan as you see fit. If you have solutions or advice to address those holes and problems, even better!!
The overall idea has merit. But in the spirit of pointing out problems:
Step #1 may be unethical unless you're honest and transparent about your intentions with the flooring contractor. Getting hired for 3-4 weeks of on the job training, with no plan to stay, only to become a competitor...I don't think this is a good way to build a reputation, at least not the one you need. This matters because much of your business comes via word of mouth.
Also, 3-4 weeks is not really enough time to learn. It's not about the total sq. footage of flooring, but rather, the variety of situations and challenges one encounters along the way. You may be able to slap out 4000 sq ft of flooring no problemo, but can you deal with lots of tight/odd corners, structures that are not quite square, problematic subflooring, moisture problems, and so on? If you enjoy the work, why not work for someone for 1-2 years before going all-in starting your own bus.? This will also give you a real sense for doing this type work day in and day out. And it will build your credibility as a flooring installer.
Licensing, insurance, bonding, workers comp., liability, building codes, regulations, taxes: These all become your problem the instant you go from doing work in your own home or within the umbrella your friend's business and start offering your services to the general public. Have you realistically factored these into your profit estimates?