How to set space usage alert for database using SQL Server 2012 with Amazon RDS as managed service?
You could create a SQL Server Agent Job which will be run daily and check the free space by using a query like below:

USE [YourDatabaseName]

/* Size in MB */
DECLARE @Info TABLE (
    [Size]          decimal(12,2),
    [SpaceUsed]     decimal(12,2),
    [SpaceFree]     decimal(12,2)
)

insert @Info ([Size], [SpaceUsed], [SpaceFree])
SELECT
    [Size] = ISNULL(CONVERT(decimal(12,2),round(f.size/128.000,2)),0)
    ,[SpaceUsed] = ISNULL(CONVERT(decimal(12,2),round(fileproperty(f.name,'SpaceUsed')/128.000,2)),0)
    ,[SpaceFree] = ISNULL(CONVERT(decimal(12,2),round((f.size-fileproperty(f.name,'SpaceUsed'))/128.000,2)),0)
    --,GETDATE() as DT
FROM sys.database_files f
    CROSS APPLY sys.dm_os_volume_stats(DB_ID(), f.file_id) vs
WHERE f.name = 'YourFileLogicalName'

/* Free space less than  5GB */
If (SELECT TOP 1 [SpaceFree] FROM @Info) &lt; 5120 BEGIN
    /*
        Anything is suitable for you:
        - send email
        - raiserror
        - write log
        .......

    */
    EXECUTE dbo.KickDBAToAwakeHim
END


Maybe, it has sense to create some table and write the values there every day to have information about how the space is changed.