Is "a slightest glimpse" gramatically incorrect?

"Of all the worst things, this is THE. WORST. POSSIBLE. THING!"

The grammar is wrong. The usage is correct. And that makes perfect nonsense.

Sometimes people like to abuse grammar. Doing it intentionally for emphasis is not the same as using it incorrectly out of ignorance.

The best example of this is double negatives. "I ain't no snitch" doesn't mean I am a snitch. It means I, really, am not a snitch. It's stylistic. It adds flavor. It's abuse of grammar. It might get you corrected. It might get you awards.

Key here is that it's characters speaking this way. Not the narrator. Characters can do what they like. The narrator is typically held to a higher standard.

If you insist on correcting it, grammatically acceptable forms include:

the slightest glimpse

and

a slight glimpse

It doesn't make sense to use the indefinite article with a superlative. It would be illogical to do so. By definition biggest means that it is the only one, so you must use the definite article - the biggest - or no article at all - Strictest discipline inhibited all creativity.

The OP's quotation should read the slightest glimpse.