So don't learn the results, and that way the results cannot bias your flipping technique.

Two options for this. If you have someone you trust completely with your bitcoin (such as a spouse), then have them note the results from the flips for you, while you don't even look. If you don't have someone you trust completely, then film the process using an airgapped device and watch the video back after you have made several hundred flips (on average with an unbiased coin you will need to make 512 flips to generate 128 bits of entropy).