The phrase "an iconic species of toothed whale" is correct as written, and it would not be correct to insert an article before "toothed whale".
Species is one of various nouns that take a bare noun phrase (with no article) as a complement of of. They all have related meanings; here are some examples:
- a species of pine tree
- a kind of machine
- a type of game
- a style of hat
- a genre of short story
When the first noun is plural, the second noun may optionally be plural as well:
- several species of pine tree(s)
- several kinds of machine(s)
- several types of game(s)
- several styles of hat(s)
- several genres of short story/ies
The species of Bengali tiger is in danger of becoming extinct.
This could be correct English, but it depends on what you mean. If you mean that the "Bengali tiger" is a species of tiger that's in danger of becoming extinct, then this is not grammatical; you should simply say "The Bengali tiger is in danger of becoming extinct" (and the fact that it's a species can be left implicit). (In real life, incidentally, it's actually called the "Bengal tiger", and is just a subspecies of tiger.)
For this sentence to be correct English, there would have to be multiple species of Bengali tiger, of which you were referring to just one. For example, the following paragraph is correct English:
This park is home to two species of finch and one species of hummingbird. Both finch species are common in this part of the country, but the species of hummingbird is endangered in the wild, so this is a rare opportunity for you to see it.
(where "the species of hummingbird" refers to the species of hummingbird found in the park).