Yes, Stylin is a legitimate app. It is a real, free iOS app built by STYLIN.AI LTD, a company registered in the United Kingdom, and it is published on the Apple App Store where it holds a 5-star average from a small early review base. The app does what it describes: it catalogues the clothes you own, builds outfits from them, shows looks on your body shape and suggests shopping picks. There is a public website, a privacy policy and a real contact address (contact@stylinai.com), so you can verify who is behind it before you download.
If you want to verify for yourself before downloading, the company is searchable on Companies House under STYLIN.AI LTD, and there is a company profile on LinkedIn and Crunchbase. The App Store listing also shows the developer name and a verifiable link to the privacy policy, which is a reasonable baseline check for any app you are considering.