DJI SPARK Instructions only instruct to connect the iPhone to the remote controller via WiFi. They do not talk about cables.
Is there any advantage to use OTG wrt WiFi iPhone-Remote connection?

With standard WiFi I start having image downlink issues at 500ms. I am wondering why I cannot reach the 2Kms as stated by DJI.

We in Europe have our Sparks in CE mode by default and there the max. range is about 500 meters. The 2 Km are only possible in FCC mode (standard e.g. in the US). You can read this in the Spark specifications on the DJI website. OTG cable has no impact on range in my opinion (although some people stick to that idea). I can not see any technical explanation why OTG should increse the range because it only replaces the WiFi connection between your device and the RC. But I believe that the OTG cable improves the data/video transmission quality between the RC and your mobile device. There are already several existig threads in this forum discussing the use of OTG. Just scroll through the topic pages a bit.
And to complete my answer: DJI until now does not support the use of an OTG cable for the Spark except for Goggles.