Adding Flavouring to sugar cookie icing:
Extracts. You can add any extract to this sugar cookie icing that you like - you choose what to use! Just remember that it will affect the consistency of the icing if you use a liquid extract, so subtract that quantity from the overall amount of milk added to the icing to compensate. If you like almond extract, you could put it in here (I don't like it so I can't recommend how much to use sorry). Just be aware that if you use a flavoring that is not clear it may affect the overall color of your icing.
Lemon. This recipe would be lovely made with lemon juice instead of milk if you wanted a lemony flavor. It may be more of a cookie glaze in terms of how opaque it is, but you can also adjust by adding in more powdered sugar to change the consistency to what you need.

Storage 
This icing is definitely best used immediately after making, but if you did need to store it, the best way would be in the piping bag - place a chip clip or something similar on both ends to stop any leaking and store at room temperature. You will have to either snip the end off and transfer the icing to a new bag or cut a new hole in the end to get rid of any crusty build up so that the icing flows easier.

Alternatively you could store your cookie icing in an airtight container or bowl with plastic wrap pressed against the surface to stop any crusting.

Can this cookie icing be colored?
Yes - you can tint this sugar cookie icing with whatever colour you want! I usually use gel food coloring but liquid will work too - just remember that if you do use liquid food coloring, that it will water down the cookie icing, so you may need to add in a little powdered sugar to get the right consistency.

Use a separate mixing bowl for your different colors of icing. If you are making multiple colors you may want to scale up the recipe slightly so that you have enough to fill each piping bag. I usually make the white icing in a larger quantity than the other colors as that is the one that gets the most use.