How can I spy on my partner’s WhatsApp chat through my phone?

You don’t. But it you try or find a way to do so, make sure you already have an attorney on retainer as what you want to do is illegal. You don’t have any right to spy on anyone, whether you date them or not. If you are so concerned about their activities on social media, the two of you have problems which are surely outside what this forum can offer you.