What can I do about slow running water in my Whirlpool refrigerator?
The filter will definitely restrict the flow, but it might be made worse if there is already a flow issue present.

Many DIY waterline install kits come with self-piercing saddle valves.  Compared to the 1/2" pipe they are fitted on (and even the 1/4" supply line), the hole they make is relatively small which reduces water flow to the fridge.

Your best bet is to not use these types of valves at all and instead solder in a tee fitting with a new 1/4 turn ball valve.  If you can't do this, an alternative is to remove the saddle valve and carefully drill a larger hole in the pipe, and then re-install the valve.