If the drill chuck is on a taper shank, using it to hold an end mill is definitely not recommended. The side loading, combined with the downward pull of the cutting forces, can walk the chuck off its taper, probably giving you more excitement than you really want.
If it's a screw-mount drill chuck that wouldn't be a problem, but a drill chuck really isn't the thing to use to hold end mills, in any case.
----------
Try to make a living, not a killing. -- Utah Phillips
Don't believe everything you know. -- Bumper sticker
Everybody is ignorant, only on different subjects. -- Will Rogers
Law of Logical Argument - Anything is possible if you don't know what you are talking about.