I start my students with double tonguing from the very beginning - third lesson or so.
The biggest killer for multiple tonguing is a screwed up embouchure. If the player is using a lot of chop tension, it is almost impossible to get the Ku to ignite the lips.
I always start with exhaled long tones - no articulation. Inhale, exhale, inhale, exhale through the mouthpiece. When the lips respond and easily produce sound, then we can add an articulated T precisely at the point between inhale and exhale. Once that works, we replace the T with a K. Once that works (days? weeks? months?), we alternate whole notes started with a T then a K. We do NOT concentrate on the articulation, rather keeping the relaxed airflow. As our reliability with whole notes improves, we move to halfs, then quarters. WE NEVER START THE NEXT STEP UP BEFORE THE CURRENT ONE IS MASTERED!!!!!!
The tongue rides on air. That is why we need the low tension embouchure before starting multiple tonguing!