When I started explaining the project’s work scope to people in the school, I learned quickly that most believed the technology classes would be my biggest challenge. One special education teacher’s comments captured the opinion I heard again and again:
"There’s no stinkin’ way you’re going to get the shop teachers to work with you on this."
What's the meaning of "there's no stinkin' way"?
It's an idiom in the US which may have some basis in historical fact but has long been disconnected from its origins, and it simply means "There's no possible way". (Though you can replace "possible" with your choice of expletives, "stinkin'" being one of the tamer ones.) – Hot Licks
Stinkin' just provides emphasis. It essentially means there's [absolutely] no way. – Jason Bassford
Stinkin' is a common euphemism for a stronger word which starts with F. I learned this from having a conversation with a police officer. He had trained himself to use stinkin' instead of the F version.
It is an idiomatic usage of stinking (adverb) to add emphasis to the the idea you want to express:
to an extreme degree
- got stinking drunk
(M-W)
As general intensifier, a euphemism for damned, fucking etc, its usage dates back to the beginning of the 20th century according to Green’s Dictionary of Slang:
1908 [UK] A.N. Lyons Arthur’s 61: Well, I knowed ’im for one o’ them furrin-born beggars be ’is stinkin’
