I was wondering if it is possible to connect to a MySQL database to perform changes on a table from a firebird DB trigger? I have looked the On External command but it seems to only work for another firebird database.
There is nothing built-in in Firebird to support connecting to other database systems. The EXECUTE ... ON EXTERNAL is only for connecting to other Firebird databases.
In Firebird 2.5 and earlier, you might be able to use UDF (User-Defined Function) to do this. However, you would need to develop this yourself.
In Firebird 3, you could also use a UDR (User-Defined Routine) to do this, but you would need to develop this UDR yourself. You can do this in Java using fbjava (warning: alpha version, and not under active development), in C# using FbNetExternalEngine (note: commercial product), but you can also develop in C, C++, Pascal and other languages that support native bindings. Unfortunately the API for that is poorly documented.