I notice a lot of people asking whether or not their fish can breed with this or that so consider this a guide to answer your question. Assuming you can get two fish to pair up and spawn, this will help determine whether or you not you will get viable fry from the pairing.
Remember that American Cichlids are essentially split up into two categories: Central American and South American.
1. All Central American Cichlids can hybridize with any other Central American Cichlid - Until it is proven otherwise, assume all Central Americans can hybridize with one another.
2. All Central American Cichlids can hybridize with any Hybrid Central American Cichlid - Most commercially sold hybrid cichlids are of Central American descent and should be considered Hybrid CA Cichlids. This includes Parrot Cichlids, Flowerhorn Cichlids, and Red Texas Cichlids.
Exception to the rule: Sterility occurs in hybrid cichlids commonly in males and occasionally in female, Parrot Cichlids being a great example of this as nearly ever single male is sterile. A sterile parent will not produce viable fry.
3. No South American Cichlid can hybridize with any Central American Cichlid - Until it is proven otherwise, assume that no South American Cichlids can hybridize with any Central American. No South American Cichlid has ever been confirmed to successful hybridize with any Central American Cichlid, any case of this happening successfully has been word of mouth.
Exception to the rule: Cichlasoma Festae can successfully hybridize with any Central American Cichlid. Cichlasoma Festae is essentially a Central American Cichlid living in South America.
4. No South American Cichlid can hybridize with any other South American Cichlid - Until it is proven otherwise, assume that South American Cichlids can not hybridize with any South American. No South American Cichlid has ever been confirmed to successful hybridize with any South American Cichlid, any case of this happening successfully has been word of mouth.
Exception to the rule: Same genus South American Cichlid can potentially hybridize with one another. For example a Green Terror (Aequidens Rivulatus) can hybridize with a Blue Acara (Aequidens pulcher).
Some example:
Firemouth (CA Cichlid) x Green Texas (CA Cichlid) = Viable Fry
Flowerhorn (HCA Cichlid) x Jack Dempsey (CA Cichlid) = Viable Fry
Synspilum (CA Cichlid) x Festae = Viable Fry
Severum (SA Cichlid) x Red Devil (CA Cichlid) = No Fry (And no this is not how Blood Parrots are made....)
Green Terror (SA Cichlid) x Oscar (SA Cichlid) = No Fry
Now there is the occasional rumor about CA Fish A breeding with SA Fish B and getting fry. One notable example of this is Convict x Severum, there have been a few reports of this happening. Until it is 100% proven to be true, I choose to be skeptical.
And as always, practice safe hybridization. Please do not breed similar fish and pass them off as one or the other. Midevil is a good example of this.