It is hard to understand your question. I will try to address every part of what you wrote.
If you're asking where PokemonDB gets its data, you can find out here. It is from dataminers and ROM hackers -- some of that work was probably done by Pokemaster (owner of PokemonDB) himself.
If you're asking whether it is a problem to use data from PokemonDB, then the answer is no. PokemonDB does not own data about Pokemon, nor does any other website. You can do what you like with it, but it is nice to credit where you got the info (as the page you linked does).
The most convenient way to get Pokemon information is via PokeAPI.