Affiliate sales via a podcast are a bit harder than with written articles because folks need to go specifically to your link on their own as opposed to just clicking in the article they're reading.
You might be doing this already, but be sure to set up an easy url for them to use such as yourdomain.com/convertkit37 that redirects to your affiliate link.
I usually see two tactics used by folks to incentivize their audience to use their affiliate link. The first is that you provide some sort of extra value or bonus if the person uses your link. This could be a PDF resource, it could be a service you provide related to getting them started with ConvertKit, it could be a 15 minute coaching call, it's up to you. For this, you can have folks forward their ConvertKit receipt to you to get the incentive.
The second is just being very upfront about the fact that the affiliate link supports your ventures and that them using it helps keep things running as opposed to asking them for a subscription fee or such.
I will note that with ConvertKit now offering a free plan, many affiliate referrals won't turn into paid commissions, which makes the effort-vs-reward equation a bit different if you're offering an incentive. Giving every referral a coaching call might not scale if very few of them end up as paid customers and commissions. You'll have to decide what works for you.