There's a flower that grows in myriad places : Rose is found in multitude of varieties and has thorns on it!
It's in a disease, it's found upon faces - AtherosclEROSis (I was thinking ROSEola and rosy cheeks)
It's found in the one who accuses a thief - pROSEcutor
It's found in the one who switches belief - pROSElytism
It's found in all those who call themselves straight - heteROSExual
As well as a very short timespan to wait. - micROSEcond
It may be a hip or a drink that you boil. - ROSEhip (I was thinking tea rose for the second half)
Search in the sundew and the stuff made from oil. - dROSEra, keROSEne
As Deusovi points out, the title can be restated as "A Puzzle That Rows In Rows", punning on the solution.