Most apps on Smartphones and tablets do require certain permission to run, and some Flashlight apps do ask for a lot of permissions, but I don't think it is a huge thing to worry about.
Note that any app can gather information about you, and companies like Google have been doing this for years (they make a note of every search you do to build up a profile of you, they also monitor your emails for clues to help them target their advertising).
But many companies gather information about what you do (Facebook, Microsoft, and so on). All the time we are on the internet companies are tracking what web pages we visit, how long we spend on them, what we search for and so on.
Even supermarkets track what we buy and how often we shop by use of their store cards (Tesco Clubcard, Nectar Card etc)
If we all worried about what data was being gathered about us we would never use the internet or our smartphones or go shopping.
There is an article about Flashlight apps on the Android web page (Android runs on many Smartphones and Tablets) and they say it is not a problem.
See here:
http://www.androidauthority.com/are-all-flashlight-apps-really-out-to-get-you-566448/