On Android Stackexchange app there is no apparent way to delete your own Question (even if there are no Answers) or to delete your own Answer. (It is possible to delete ones own Comments, by touching it to select it and then touching the Trash Can icon at top). On the other hand, there is a "..." (more) link below the Question which contains an option to Open in Browser.
In mobile version the web page presentation of your Question includes a "delete" link below your Question (but above the author/asked/edited byline), between "close" and "flag" link options. Correspondingly the mobile version puts a "delete" link below your Answer, between the "edit" and "flag" links.
I successfully deleted (and then undeleted) this Question of mine using the mobile web page approach as outlined. I haven't tested deleting one of my Answers in this corresponding manner (yet), but I will get around to it soon and report if there are difficulties encountered.
Occasionally a user will request a post be deleted after having lost their login used to create that post. Some caution is needed in these cases because of the risk of identity spoofing, and I generally refer the user to the FAQ on how to merge multiple accounts. If the case seems compelling that the user requesting deletion is the same, I have at times flagged for moderator attention giving my reasons for that conclusion and recommending deletion (if otherwise appropriate).
Of course, from Review one can vote/recommend to delete if the post qualifies for such treatment even aside from the OP's wishes.
Bug reports concerning the Stack Exchange Apps, either Android or iOS, are currently being handled through Questions posted at Meta.SE. Searching for "Stack Exchange App" and [bug] there will give you an idea of what has already been reported and fixed. At a glance I did not find any reports connected with inability to delete ones own posts. Be sure to specify the version of your app and how to reproduce the problem.