Essential oils- I'm assuming they are volatile so I would run those on GC-MS.
Alkaloids and flavanoids generally run well on HPLC. You _may_ need to switch to negative mode to see flavanoids although I've seen them in positive mode. Please note that I'm speaking generalities since some compounds of each group could be difficult to elute or coelute with other compounds.
I personally like to do initial purification of alkaloids with strong cation exchange columns and initial purification of flavanoids on strong anion exchange columns. I then do any further purification on C18. The initial purification on the ion exchangers removes a lot of compounds that could co-elute.