It depends
Smoke flavouring is condensed smoke, which on its own has nothing to do with grain. The problem is the carrier: smoke is a vapour and has to be fixed to something to become a powder, and barley malt flour is one of the materials used to do it. Barley is not a major US food allergen, so it need not be declared — meaning a label can read "natural smoke flavor" with barley inside it and be entirely legal. A gluten-free claim on the package resolves it; nothing else on the label will.
Because the answer depends on the rest of the label, scanning the actual product is the only way to resolve it — CiCi checks for a gluten-free claim, the allergen statement, and which agency regulates that label, then tells you which way it lands.
liquid smoke is one of the names CiCi tracks for Smoke flavoring. Ingredient lists use many names for the same thing, which is a large part of why gluten slips past careful readers.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.