Those traits are not useful for secret communication.
Firbolgs and forest gnomes are not beasts nor plants so Speak with Small Beasts and Speech of Beast and Leaf doesn't work to communicate between them. Even if you ignore that, neither trait allows for secret communication.
Speak with Small Beasts:
Through sound and gestures, you may communicate simple ideas with Small or smaller beasts.
If someone repeatedly gestures in a certain direction, I will eventually understand I need to go in that direction, but a rat never will (unless it is a trained rat). Whereas if a forest gnome does the same, even a rat can understand.
Speak with Small Beast doesn't need to work on other people, because people are already capable of communicating simple ideas with each other through sounds and gestures. Anyone person who notices sounds and gestures could understand because they are not codewords and secret signs.
Speech of Beast and Leaf:
You have the ability to communicate in a limited manner with beasts and plants. They can understand the meaning of your words, though you have no special ability to understand them in return.
If someone says "Go over there", I can understand what they are saying if I understand the language, but a dog or cactus will never understand (unless it is a trained dog). Whereas if a firbolg says the same, even a cactus can somehow understand.
If Speech of Beast and Leaf worked on creatures other than beasts and plants, then the firbolg would be capable of one-way communication with anyone through meaningful words, but this trait doesn't let the firbolg choose individual targets, so anyone who overhears those words would also understand.
Allow your players to communicate secretly anyway
The idea that a party of firbolgs and forest gnomes can communicate secretly with each other is fun and thematic. A couple days of prep-work to come up with some code words and unique gestures is all that is necessary to communicate some simple concepts. Other people would generally be capable of noticing this communication, but the meaning would be obscure.
Dismissing this prep-work as a basic understanding between nature-minded races is entirely within the purview of the DM.
Also note that this is different from Thieve's Cant, which allows people to pass hidden messages through seemingly normal conversations and hidden signs.
During your rogue training you learned thieves' cant, a secret mix of dialect, jargon, and code that allows you to hide messages in seemingly normal conversation. Only another creature that knows thieves' cant understands such messages. It takes four times longer to convey such a message than it does to speak the same idea plainly.
In addition, you understand a set of secret signs and symbols used to convey short, simple messages, such as whether an area is dangerous or the territory of a thieves' guild, whether loot is nearby, or whether the people in an area are easy marks or will provide a safe house for thieves on the run.