Color mode can't be RGB, right?
RGB printers do exist, such as the LumeJet S200 so the request for RGB profile could be accurate or your printer will be using a Direct to Garment flatbed printing process. This would also be a good time to ask your client for your printer contact for clarity on what they're needing. Having a middle person can cause errors and you will spend double the time trying to figure out what they need. There is nothing wrong with asking the client for the printer contact since this approach ensures you deliver what your client needs.
I've expanded all the outlines of the objects - is it considered to be
a flattened layer?
No it's not considered flattened. Also, as I've grown up as a print designer I would encourage you to get in the habit of separating your layers by color, regardless if you're printing RGB, CMYK or Pantone. This is a very good habit and print production will love you for it. Nothing was more frustrating then getting a flattened EPS that I would have to separate to make plates for screen printing. However, I somewhat wonder if the client's printer is going to request a flattened TIFF file.
Is it possible to delete channels in Illustrator?
Somewhat sounds like you're having to provide a TIFF for printing perhaps. I haven't done this in Illustrator but I've used ImageMagick to remove the alpha channel:
convert in.png -background black -alpha remove -alpha off -resize 1024x1024 out.png
Also, a similar question may help you: Pantone to RGB print on fabric?