Subscriptions work differently on iOS than other platforms on which Twitch is available. You'll need to buy an iOS Sub Token through the app, which is good for a Tier 1 subscription for a month. You can redeem up to 12 at a time per streamer to keep a subscription to them going for a year.

The tokens cost a little more than desktop subscriptions to account for Apple's App Store fees. They're $5.99 instead of $4.99, but you can buy two for $8.99 until the end of the month. It doesn't seem you can use Twitch Prime subscriptions through the iOS app either.