Are you supplying film/plates to the printer? Can you just give them the files and let them handle it? Or does "printer" mean "pressman?" Maybe tha'ts a UK vs. US thing.
I wonder wether FM screens are often used in flexo, given the nature of the process. If FM is okay, I agree with David_Modprint: make the white and yellow FM, perhaps with a larger than normal dot size if FM is problematic for flexo (I'm assuming you'd need to make two inks FM, since you have six and you wrote that all interact).
If you need to stick with conventional screening, you can treat Pantone 300 as an additional process color, then you can max out the black generation and use only two angles for the hue inks (cyan, magenta, yellow and Pantone 300) because aside from black and white, you would only have cyan + Pantone 300, Pantone 300 + magenta, magenta + yellow or yellow + cyan. The cyan and magenta could both be 15 degrees, and the Pantone 300 and yellow could both be 75 degrees. This leaves 45 degrees for your black and 0 degrees for the white, or vice-versa depending on which is stronger. Pantone 300 should then be printed before magenta, cyan and black in the ink sequence to preserve the transparent interactions with the normal process inks. You can send me a sample of the artwork containing an area where all inks interact, and I'll send you back an example.
Barring FM screening and using Pantone 300 as a process ink, and assuming you have interacting screens (not just solids) between every possible ink pair, your options would be:
Identify the two process+spot pairs that have the least interaction and make the spot angle the same as the process angle, risking the moire.
Make the yellow and white different screen frequencies at two different angles that would each be the same as another ink, which may not eliminate moire and could make it worse, depending upon how close the ratio of the frequencies is to a simple harmonic ratio. I usually attempt to preview moire by printing a small area in question from the 2400 ppi plate image to a 600ppi inkjet at 400% size.
Convert the image of two inks to line art, rendering tints as coarse alternations, similar to wood cuts or the old AT&T logo. This can be done semi-automatically with Photoshop.