Each time you unlock a new fighting move, Flame Face will have a set of combo trials for that move you can try and pass for a gold reward. He can be found at the Flaming Tequila Bar/Flame Face's Fight-a-torium on the right side of the town of Pantanillo in Los Manglares.
You can either do each move's set of trials right away or wait until you've unlocked them all and do them all at once. The last move you will need to unlock for its trial is the Pollo Slide which you will unlock in the Pollo Illuminati which is reached after escaping Prison "El Corazon".
These combos do get progressively harder but as C3LLDW3LLER mentioned it's best not to rush and to try and find a rhythm. If you a fail a combo you only start from that particular challenge, not the beginning of that move's "chain" which allows for quick retries. As a tip, don't do only the buttons showed on the screen as it's best to re-position Juan either on the ground or the air with the left stick during some combos. For example, going from Dash Punch to Head Butt may cause you to Head Butt beyond the enemy and so a quick adjustment should be made between the two attacks.