Yes, this is gluten free
Distillation leaves gluten protein behind. All of these are gluten-free even when the starting material was a gluten grain.
Dilute acetic acid, made by letting bacteria ferment alcohol. The alcohol can come from almost anything that will ferment — apples, grapes, rice, malted barley — and in the US "distilled vinegar" with no other word in front of it is usually made from corn or from grain alcohol.
Because the starting material sometimes is a gluten grain, and because malt vinegar sits on the same shelf and is a genuine problem. People encounter the warning about malt vinegar, generalise it to vinegar, and end up avoiding a category that is almost entirely safe.
Every vinegar in a normal kitchen is fine: white, cider, red and white wine, balsamic, rice. The one to leave alone is malt vinegar, which in the UK and Ireland is the default on chips and in a great many sauces, pickles and crisp flavourings. Reading a British label for vinegar is a different job from reading an American one for exactly that reason.
CiCi tracks malt vinegar as a separate entry with its own verdict rather than treating vinegar as one thing. The scanner will clear a label carrying distilled or wine vinegar and flag the same label if the word malt appears in front of it, which is the distinction that actually matters.
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.
The aisle guides below cover Distilled vinegar in context — which is usually the more useful question, because an ingredient rarely appears alone.
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.