"Prohibition against stealing," was the phrase that was being used. I get what the speaker was trying to say, but I'm just wondering if it is grammatically correct or if it could have been worded better.
A double negative is a grammatical construction occurring when two forms of negation are used in the same sentence. - wikipedia
Your example isn’t a double negative because there aren’t two forms of negation in your quote. There isn’t even one form of negation in the quote.
Syntactically, prohibition is not a negated term. To be a negated form, it would need to be something like non-prohibition.
Likewise, against isn’t a negated term. It is just a preposition to relate the word prohibition to the thing prohibited.
“Prohibition against” is not a "double negative" (or rather, it isn't an example of negative concord)*. Compare “a battle against”. Even though the preposition “against” often is used to express that something acts counter to something else, it is not a negation.
As other answers mention, the word “prohibit” also does not contain any morpheme explicitly dedicated to negation. But “prohibit(ion)” does have some connection to negation in that it can license a negative polarity item like “at all”: we can say “they are prohibited from driving at all” while most speakers can’t use at all in a sentence like *“they are permitted to drive at all”. (See Greg Lee's answer to "Is “prohibit” a negative word?")
The Google Ngram Viewer indicates that “against” is the second most common preposition found after “prohibition”. The most common is “of”; you could say “prohibition of stealing”. Other possibilities are “prohibition on” and “prohibition from”.
*"Double negative" is a fairly ambiguous term: it is often used to refer specifically to a construction that is excluded from the grammar of standard English ("I don't have no money" = "I don't have any money"), but a sentence like "I didn't say that he didn't come" has two negative words corresponding to two separate negations, which is completely permissible in standard English. I prefer the term "negative concord" to refer to the phenomenon seen in "I don't have no money" = "I don't have any money"; another benefit of the term "negative concord" is that it doesn't specify a particular number, since we can see more than two negative words in a sentence with concord: "I didn't tell nobody nothing" = "I didn't tell anybody anything."
A double negative? No. It's not even a single negative. Neither "prohibition" nor "against" is a negative. Examples of negatives include but are not limited to:
A negative in grammar expressly contradicts what the negative is modifying so as to indicate an absence of existence.
To be clear, "prohibition" is the positive action of some authority imposing a rule that bars a thing or activity. "No prohibition" would be a negative because it would indicate the absence of existence of prohibition. Likewise, "against" is a preposition that positively situates the relative positions of the subject of the preposition and the object of the preposition. "Not against" would be a negative because it would indicate the absence of that situation.
"The helmet failed against the crushing weight of the brick falling on it from ten stories up." In that sentence, you may view "failed" in a negative light, but it's not grammatically negative because it is indicating the positive action of the helmet caving in instead of performing the positive action of resisting or repelling the crushing weight. Likewise "against" positively posits the crushing weight in relation to the helmet. Were it "The helmet failed not against the crushing weight..." that would be a negative. Were it "Not the helmet failed against the crushing weight..." that would be a negative. A double negative would be, "It wasn't the helmet that didn't fail," which would be wrong if the meaning were suggesting that the helmet failed but something else didn't.
No, it's not a double negative. "Against" doesn't mean "not", and any negative sentence it has is applied to "stealing", not "prohibition". It is at most a negative concord. Just because a word "goes with" negative senses doesn't make it a negative. For instance, consider "There are some" versus "There are not any". When you switch from positive to negative, "some" changes to "any". That doesn't mean that "any" is a negative, or that "There are not any" is a double negative.