As others have indicated it it a very bad idea mill with end mills in a drill chuck. The drill taper is not designed to hold with a side load. It is designed to drill (up and down) so the forces press the drill chuck onto the taper when drilling. You can get a set of R8 collets very inexpensively from ENCO (
www.use-enco.com).
6pc R8 collet set DD231-4606 currently on sale for $19.95
11pc R8 collet set DD231-4611 on sale for $36.95
23 pc R8 collet set DD231-4624 on sale for $77.95
The $20 6pc set should serve you well and be much safer than milling with a drill chuck.