About a month ago, I changed a GoDaddy domain’s nameservers to use CloudFlare. However, since CloudFlare went into effect, any contact forms filled out on the website are not forwarded to the domain-based emails, yet are still forwarding to @gmail emails. The domain-based emails can receive emails from any other addresses, just not through contact forms. I suspect that it has to do with having incorrectly configured DNS records.
Your MX record looks all right and if you generally can receive email, I would say that should be correct.
So your issue only is that submitted forms do not end up in your @apollosunguard.com inboxes, correct?
You said those emails get correctly forwarded to Gmail, right? By whom do they get forwarded? By aforementioned inboxes or are you sending those form emails separately to Gmail?
Right now my best guess would be something spam related. Are your emails sent with an @apollosunguard.com sender? In that case the emails might get rejected by your mail server. You should probably configure at least a proper SPF record for your domain.
While doing that, you should also remove the two NS records in your screenshot, as they can lead to DNS errors.