In your video, your measuring device is too close to the kindle. It also has a directional antenna that is not pointing at the kindle, making the measurement less accurate. RF radiation drops off rapidly as distance increases. Unless you use your kindle as a pillow, it should not be a problem. Whereas cellphones ARE held close to your head and subject your brain to much more radiation due to very close proximity, and at a much higher power level to reach a distant cellphone tower
I would not worry about the kindle wifi. It is mostly "receive only" with only very short transmit bursts. Radiation damage is cumulative, and I would worry about talking on a cellphone next to your head for extended periods much more than using kindle wifi at arm's length with only occasional web page refreshes or other wifi activity.
To measure the kindle wifi transmit power EXPOSURE accurately, place the kindle where you store it at night, and place the meter on your pillow with the antenna pointed at your kindle. Then measure it. And remember that it is the AVERAGE power over time (not the PEAK power) that counts (except in extreme cases like over-the-horizon radar transmitters).
2.4 GHz energy is used to heat water molecules (in a microwave oven), which is why it is available for wifi devices. The most damage it could do is cause cataracts if your eyes get heated too much, and it would take strong microwave radiation to do that (like from a microwave oven, not from a battery powered kindle). In the olden days, military radar operators would stand in front of the microwave radar dish to warm up, and a melted chocolate bar in a pocket was the inspiration for microwave ovens. It is not as dangerous as ionizing radiation from nuclear decay. It is only a problem if sensitive organs get overheated (especially the corneas of the eyes). On the other hand, low frequency electromagnetic energy (such as under power lines) can have biological effects. It can promote bone healing, and it can make crops under it grow faster. Perhaps it can cause cancer from uncontrolled stimulation of growth (especially in children). But microwave energy is generally safe at low levels like wifi uses.
It is also interesting that the bioinitiative.org domain name is owned by somebody who works for a WIRED communications provider. Using a "non-profit" website to spread FUD against the competition (wireless communications providers) perhaps?