Good question! The free Twitch Prime skins usually come out a few weeks after new skins are released. Twitch usually releases new skins at the start of the month, so you can expect to see the free Twitch Prime skins some time after that.
Twitch also occasionally releases skins in "drops", where special skins are available for a limited time. You can check here for upcoming dates for the next Twitch Prime skin drops: [https://twinfinite.net/2020/05/twitch-prime-loot-drops/ ]
Additionally, some new skins are released alongside major events. May and June usually have events going on where new skins will appear as part of that. You can use the Twitch official website or some other sites like [https://www.3000up.com/skin-release-calendar/tw/ ] to keep up with upcoming events and skin releases.
Finally, sometimes Twitch will even surprise us with limited-time Free Twitch Prime Skins. These are skins that last for only a few hours, so make sure to check the Twitch Prime website and social media often to make sure you don’t miss out on them.
Hope that helps!