Hey Lucas, how are you? I hope you are doing just fine!
All these phrasal verbs have the same meaning, which is ''to casually read through a document, magazine, or book without paying close attention to it''. You can choose any of them to be used in a sentence:
1) ''Flick through'': to turn quickly through the pages of something. In this case, the word 'flick' is used in the sense of 'look through the parts of something by making quick movements with the fingers.'
E.g.: ''I have only had time to flick through the manuscript, but it looks okay.''
E.g.: ''She flicked through the newspaper, looking only at the advertisements.''
2) ''Flip through'': to browse through something, without paying enough attention to it. This expression uses 'flip' in the sense of
'turn over pages.'
E.g.: ''She flipped through the magazine while she waited.''
E.g.: ''I had just started flipping through a magazine when the receptionist called my name.''
3) ''Thumb through'': to go through some reading material quickly or superficially, turning from page to page with or as if with the thumb.
E.g.: ''I thumbed through the directory for my dentist's phone number.''
E..g.: ''I've only thumbed through this book, but it looks very interesting.''
*NOTICE: ''Leaf through'' is another idiom which can be used to convey the same idea as the other expressions above. This expression employs 'leaf' in the sense of 'turn over the leaves of a book', a usage dating from the mid-1600s.
E.g.: ''I leafed through a magazine while waiting to see the doctor.''
E.g.: ''There she sat, leafing through the various catalogues.
Hope you have understood!