Is this an idiom? I heard of it on a TV show. Sounds like an idiom, because there's no barbecue apron at the moment of speaking.
Just because that's on your barbecue apron doesn't make it true.
added information:
Mom is leaving for night shift. She tells her husband, "Here's Charlie's schedule. It tells you when to feed her, when to change her, and when to put her down." The husband responds, "Honey, would you relax? Big dad's got this all under control." Then Mom says the sentence above.
It's not an idiom.
You haven't provided the wider context of the quotation which would surely explain. If I had to guess, I'd say that the speaker has already seen the other person's BBQ apron and it says something like "chef". So, if the person is claiming to be a great chef, the suggestion is that it might say that on their apron, but it isn't true.
BBQ aprons are typically humourously boastful, with slogans like "BBQ King", "Boss of the Sauce" or "The Grill Master".
No, this is not an idiom.
Wikipedia defines an idiom as
An idiom is a phrase or expression that typically presents a figurative, non-literal meaning attached to the phrase;
This phrase is conveying a literal meaning, the only thing not immediately obvious to a fluent speaker who may lack cultural references is what a barbecue apron might be. Once that is resolved, the phrase is literal rather than figurative.
Potentially, there is no actual BBQ apron. And the speaker is responding to some pithy phrase used by another character that might be printed on an apron. This moves it closer to being an idiom.
The word idiom is sometimes used to simply mean a common phrase or expression. Even in that case this phrase would not be an idiom (yet?) because I've never heard it before.
