Rough estimation of power consumption in an electronic design
Adding the maxima (from the normal operations sections) of your ICs will yield a (very conservative) upper bound on your current consumption. 

To get at a more realistic value you can either measure, or figure out how the actual values vary with the circumstances. Power voltage, temperature, operating mode, and clock frequency often have a big impact.

Start with the list of the power consumptions of all your componets, sorted from high to low. Concentrate of the top entries, you can probably ignore the tail of the list. The 'attack' on the individual components requires experinece, skill and insight, and depends a lot on the type of component. 

In a comment you mention the AT25SF041. Its current depends on its mode of operation (power-down, stand-by, active). The conservative estimate is that it is always active (max from the table: 16 mA). If this puts it on top of the list, you need to get more info about how it is used.

If you have a lot of components that attribute roughly the same current, and you can live with &lt; 100% working products, you could use the typical values instead of the max ones, or do a distribution-based addition (assuming some distribution..). 

Another interesting aspect is whether you need the average of the peak power consumption. A good design probably needs to take both into account.

PS thumbs-up for using the normal-operation values, be be aware that we see too many questions (and sadly even answers!) here that use the "absolute maxiuma", which are almost never relevant.