There are numerous papers out there on these drugs. Check out the veterinary drug residue literature for methods with fairly low detection limits. Some issues you may have with LC-ESI-MS are
1. Chloramphenicol is a negative mode analysis. Depending on your instrument, formic acid may suppress the signal. Otherwise, it is "nice" compound to chromatograph in reverse phase (doesn't really even need a modifier...). Extracts nicely with EtOAc or ACN.
2. Kanamycin is a bit trickier to analyze. I've done it with HFBA in the mobile phase using a RP column. You pretty much have to dedicate your mass spec though--HFBA ruins it for negative ion work and can suppress positive ion analysis, too. HFBA is nearly impossible to get rid of, though I've heard replacing diaphrams on LC degasser helps (in addition to replacing all other plumbing and doing a really thorough source clean). If I had it to do over again, I do HILIC for aminoglycoside analysis (that ought to make at least one regular participant in this forum happy

). Aqueous TCA extracts aminoglycosides nicely, but you do want to minimize TCA in the MS--same problems as HFBA.
I'm not sure you'd be able to pull off residual analysis for both of these compounds in one assay....