Make sure the Na2CO3 is already dissolved before you add it to the reactor or you'll coat the solid Na2CO3 with CaCO3.
I would mix the two streams in one tank and use a second tank for solid/liquid separation if required. The reaction will be very fast, the tank residence time will be more about allowing sufficient time for mixing/preventing short circuiting rather than the precipitation time. I assume you have access to the waste stream? A quick lab test will give you an idea of how fast the reaction is. Have the waste stream mixing, add enough CaCl2 to be in excess (say 5% excess), sample and filter 30 seconds later and check the residual CaCl2 level. My bet is that you would already be at equilibrium.
If you don't have access to a lab to analyse for calcium- take your sample, filter and then add more Na2CO3 and visually check for additional precipitation.
If you don't have access to the waste stream- make up an artificial one. Both chemicals are available at your supermarket (Damp rid/damp remover is normally CaCl2 and washing soda is Na2CO3)
Before you get too carried away though- how important is the answer (i.e. how big is your waste stream, what's the concentration of CaCl2, what's your target concentration).
If it's a small flow then the cost will be relatively insensitive to the required residence time. The larger the flow the higher the justification for lab/pilot testing.
As a chem eng/metallurgist the first part of any answer I give starts with "It Depends"