Why is it said that Amazon creates 20% of the oxygen production of the world, when it accounts with less than 14-12.8% of the forest area?
I cannot find any language in peer-reviewed literature (as far as publicly accessible) that makes the 20% claim reported in the question. I therefore consider this claim to be of obscure and dubious origin.

About 50% to 55% of the oxygen produced via photosynthesis is estimated to come from the world's oceans, as reported in the following two papers:

Curtis A. Suttle, "Marine viruses -- Major players in the global ecosystem." Nature Reviews Microbiology 5 (10): 801-12 (2007)


  The oceans cover more than 70% of the Earth’s surface. They control the climate, provide a significant amount of the protein that is consumed globally and produce approximately half of the Earth's oxygen.


A. Yu. Borisov, L. O. Björn, "On oxygen production by photosynthesis: A viewpoint", Photosynthetica (2018) 56: 44


  We also find that the ocean produces 22% more oxygen than the land surface.


According to an expert quoted by the BBC, about 16% of the land-based oxygen production from photosynthesis occurs in the Amazon basin:


  A large proportion of the world's oxygen is produced by plankton, explains Professor Malhi. He says of the oxygen produced by land-based plants, about 16% comes from the Amazon.


Is this claim plausible? Based on the reported size of Amazonian forests at 6-8 million km2 and the world's total forested area of about 40 million km2, I am inclined to answer in the affirmative, although not all of the land-based oxygen production occurs in forested areas.

Yale's Global Forest Atlas:


  Amazon basin is the largest tropical rainforest in the world, covering a size approximately equal to the lower 48 United States. 6-8 million square kilometers of forest house approximately 10% of the world’s biodiversity and 15% of its freshwater.


Based on data from the FAO suborganization of the UN


  Forests cover 31 percent of the world’s land surface, just over 4 billion hectares.


The area of a forest and its oxygen production are unlikely to be in strict linear proportion to one another, as the rate of photosynthesis should depend on such factors as solar irradiation (which varies with latitude and cloud cover) and temperature (in boreal forests) or the seasons (for deciduous forest in moderate climates). The density of a forest will likewise be influenced by the availability of water and nutrients.

How do scientists estimate the amount of oxygen produced via photosynthesis? Best I can tell from a perusal of the literature this is done indirectly by estimating total biomass, which itself is determined by a combination of satellite data and on-the ground measurements. Such estimates carry a non-trivial amount of uncertainty.

Nowak, David J., Robert Hoehn, and Daniel E. Crane. "Oxygen production by urban trees in the United States." 
Arboriculture &amp; Urban Forestry. 33 (3): 220-226. (2007)


  The net amount of oxygen produced by a tree during a year is directly related to the amount of carbon sequestered by the tree, which is tied to the accumulation of tree biomass.


S.S. Saatchi, R.A. Houghton, R.C. Dos Santos Alvala, J.V. Soares and Y. Yu, 
"Distribution of aboveground live biomass in the Amazon basin",
Global Change Biology (2007) 13, 816-837


  To determine the spatial distribution of forest biomass of the Amazon basin, we report a method based on remote sensing metrics representing various forest structural parameters and environmental variables, and more than 500 plot measurements of forest biomass distributed over the basin. [...] We estimate that the total carbon in forest biomass of the Amazon basin, including the dead and belowground biomass, is 86 PgC with ± 20% uncertainty.