I initially experienced similar problems with my 2 speeder kick start. The whole aparatus is a bit flimsy and I found that I was cautious about giving it a really good kicking! I was always told that if you kick it twice and nothing happens than there is a problem – advice which is no doubt well-meaning but often a little detatched from the reality of an old bike.
After some deliberation and practice I found that the following proceedure worked and I think that I might have seen the practice adopted by an obviously knowledgeable (and aged ) 2 speed specialist at the Banbury Run one year.
The travel on the kick start (at least on my bike) goes beyond the 180 degree mark but it is difficult to kick it that far when standing along side the bike facing forward in the conventinal manner – or even for that matter standing astride. Nonetheless that extra 10-15 degrees travel is necessary.
Firstly, try kicking it whilst standing alongside but facing backwards (if you see what I mean). This operation is best done with the aid of a mate holding the bike for you by the handlebars (unless you are content to bend the rear stand). Certainly said subject at the Banbury run was so assisted.
Secondly , try to develop a measured rythmic kick (honestly!). After two or three such kicks the engine builds up a bit of momentum in turning (or at least one of the kicks falls in sync with the turns produced by the last) and hey presto !
Anyhow, that’s how it is with mine. I hope this might help.