I haven't used solidworks CAM myself, but I have used a couple of different CAM packages and different interfaces.
A couple things. First is that a Jacob's chuck is not designed for milling use. They are designed for drilling applications where the forces are strictly axial, meaning that all the forces applied to the tool and by extension to the chuck are pointed along the axis of rotation of the chuck.
I would suggest getting a milling chuck if you want to use a chuck, but collets are a better solution if you can interface them with your spindle. How is your Jacob's chuck attached to your spindle? is it a morse taper?
Regarding tool offsets:
The typical process in a machine that you don't have a tool changer for would be to post a separate Gcode file for each tool.
Set your work coordinate system (usually G54) somewhere that you can reference with each tool change. This might be with Z=0 on your machine's table or the top of your vise or the top of your stock in an area you won't machine away.
With your work coordinate system active in linuxcnc insert your tool into your spindle and secure it. Then jog to where you are going to set z=0 and use a piece of paper or a 123 block and jog downward slowly while moving the paper or 123 block around until you feel contact with the tool. Then you set this as your z=0. If you use a 123 block then it will actually be z=1" and if you use paper it will be around 0.004"