Are there any other clues the speaker had multiple elephants in mind?

Certainly not. Proper liaison is the only clue.

The oral version of a sentence without liaison (Je parle de leurs téléphones) is 100% ambiguous.

Four strategies to resolve the ambiguity in cases like this:

• Context. From what you know, do they jointly own an elephant or do they have a herd?

• Agreement. Listen for an adjective that differs in the plural (éléphant royal / éléphants royaux) or a verb that does the same (éléphant qui boit / éléphants qui boivent).

• Ask. « Parles-tu d’un seul éléphant ou de plusieurs ? »

• Echo. When you talk about the same subject, choose an unambiguous wording (Donc, pour les éléphants …) so they can straighten it out if you’re wrong.

Though I love Duolingo, none of these options is possible with their isolated sentence system.

Edit: I should add that as far as I know, this liaison is not optional, as a determiner + noun. Perhaps Duolingo’s text-to-speech system is at fault. Or maybe that rule is not always followed in practice.