I just got my results back from My Heritage. I have a picture of my Great Great Grandfather he definitely looks Chinese, his father was 100 percent Chinese and he married a Native American they would be my Great Great Great Grandparents, why am I not showing any percentage of Asian or Native American on my results? If my father were tested would it possibly show up on him since it would be his Great Great Grandfather?
If I read your question correctly, you are 1/32 Chinese and 1/32 Native American. It is not surprising that those ethnicities were not detected since you might not have any DNA from those ancestors in the regions used for determining ethnicity. See also How many generations back will specific ethnicity show up in DNA?.
Another factor is that the ethnicity results are not very accurate. You may get different numbers from different companies or even if MyHeritage changes its algorithms.
If the Chinese male ancestor is your father's father's ... father, you can have your father or your brother, if you have one, do a Y-DNA test. Similarly, if the Native American is your mother's mother's ... mother, you can do a mitochondrial DNA test.
My Heritage's ancestry calculators have issues. I would not rely on them. Download your raw data to your computer then upload it to Gedmatch.com. Wait a few days for your kit to be fully loaded. Then run their ancestry calculators and see what they say.
If the family stories are true, then it is still possible not to have ancestry markers from these 3rd great grandparents show up in your DNA. It's also possible that the family stories are not true. Checking with Gedmatch (try several of the calculators and be sure to do Oracle 4) will give you better data to work with.