in a nutshell, I believe that currently the only way to subscribe to a channel is from the channel itself. But, if i want to subscribe on a channel from another website, and track it for analytics, could be possible?
No.
The only avaiable ways to subscribe/run the payment flow are all on the Twitch website either on
https://twitch.tv/CHANNELNAME/subscribehttps://twitch.tv/CHANNELNAME/https://subs.twitch.tv/CHANNELNAME/
Which are all the same to Twitch stat tracking (just different layouts used in different ways)
You think in future could be possible? if i want to promote my streming from my website, and people want to subscribe from my site (obivious still a normal Twitch subs) and i want to know how many people subs from my site, i can’t now, right? I hope in future they will change it 
Then you need a uservoice for this https://twitch.uservoice.com/
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