It would be possible to open a phone call from your programmed skill (alexa skill service). But for sure you not just want to start the call but also that the user can speak into alexa? But it's not possible to get the voice from the user.
Amazon Alexa transfers the speech input into text.
Your skill service only get JSON requests from the amazon skill interface with intents and spoken things as text.
So there is no chance to the get the audio track from the alexa user. Also stated in the forum
- There is a feature request - you should watch this feature and vote for it.
- Or you implement something like a callbackservice that you interconnect users telephone to service customer number. E.g. via an app on the phone - see this