I have a WordPress Website with the DNS settings configured in Cloudflare and Cloudflare setting set up in the website but also I have a bunny CDN subscription, Is configuring the two options in my website will be possible, or will create any issues?
If that is possible how can I make this integration?
BunnyCDN is a PushCDN.
Cloudflare is a ReverseProxyCDN.
So they use different techniques and could be complementary. But when you combine them you basically just use BunnyCDN to soften the lows of Cloudflare as it would take less time to fetch something from an origin, that itself is a CDN.
To answer your questions:
Yes, you can use them together but it probably is not worth the effort, just use Cloudflare and you will be good to go.