How exactly did the Engineer plan to unleash the black goo on Earth?

 I think that question was answered in Covenant. Also, I think Shaw saw and experienced enough of what the goo did and rightly figured it would not be good to reach Earth.

I think she had witnessed what harm came from 10's maybe even hundred odd leaking Urns, and then having seen the Juggernaught had Thousands.

She made a Assumption of the Damage that could be done, if this Pathogen got to Earth....  We cant be sure how much damage would be caused....

But its hinted that this stuff would spread though the air and water and it would have a huge effect, we cant say it would mutate/destroy all Life... but that a large portion would be infected and that would also likely result in the spread of destruction from Organisms created from the Black Goo.

It appears the Ships have at least TWO such Cargo Holds, it could have up to FOUR

Between comments by RS, the Weyland File on the Black Goo, and Alien Covenant it is implied indeed a Full Load of these Urns would in effect wipe out most if not all life on a Planet.

Dr Shaw merely made a Assumption... but we need to remember with Prometheus many of the crews comments are actually Narrations to explain what is going on...  

From Dr Shaws, Ebola reference when she says shes seen something like this before (Pathogenic/Viral Outbreak). To Janeks talks about the Weapons Facility etc.

If someone was to work on Ebola... find a way to increase its infection to also be transmitted via same methods as FLU and if it also can spread just like FLU and Ebola so we have a Hybrid Virus that combines both of these....  with NO CURE

If the infected Fluids so the Hybrid Virus was Produced in Large Quantities so that infected substance had the same volume as we see the Black Goo Urns in Prometheus would leak.

And a Country loaded this Virus into similar Canisters in their Thousands and then Bombarded a continent like the Americas or Europe then you be sure a Epidemic would happen and Millions and Millions would die within weeks/months.  Potentially leading to Billions if infected people or fluids managed to travel to other continents.

We can safely assume the Black Goo effects are much more serious.