This really depends on what you are trying to do. Are you after specific kinases? Do you have any idea where they will be found in the cell? Do you have any idea of their abundance in the cell? What techniques are available to you? Once you answer these questions, you can then decide what to do next.

Dr. Hains, I have purified kinase that can utilize bulky ATP analogs.  I'll be performing a kinase reaction assay on cell lysates to see which direct substrates come up as hits in lysates, so kinase abundance isn't an issue as my reaction will have higher-than super-physiological concentration.  It has been shown to have targets in the nucleus, cytoplasm and at the cell membrane.  My main reason for fractionation would be to reduce sample complexity in order to enrich for direct substrates and allow for more efficient phosphorylation.  Ultimately, I can perform fractionation by either separating peptides based on ionic characteristics or subcellular localization; I mainly want to know if either is preferred for a kinase assay.

I'm a bit unclear, do you want to fractionate before or after the kinase reaction? I haven't actually done anything like this, so I can't comment on the advantage, or otherwise, of fractionation prior to the kinase reaction. However, the ultimate goal is obviously to purify phosphopeptides and there is a wealth of literature on that. If you're not sure search Martin R Larsen and phosphorylation.

If you are still interested, there is a technique called Free-Flow electrophoresis, that can fractionate native cell lysate in around 10 minutes. Afterwards it is possible to do an kinase assay in the 96 well plate that is used to collect the separated fractions.