Can a friend see how many times I have looked them up using Find My Friends I am sharing my location with some friends using Apple's Find My Friend service.

I am curious to know if they get to know how many times and when I have looked them up using Find My Friend?
As per @ Nimesh Neema answer https://apple.stackexchange.com/a/339887/46541 

Your location is sent from your device only when someone requests to see it.

It means, if you request your friends location, your phone knows his number (you shared it) and will send a "Ping signal" to find it. 

Once your friends phone receives the Ping request it will reply to you with the location data.

So theoretically YES, your friend could know you looked him up (Ping), if he has the tools and knowhow.

Some more technical stuff about it..
Officially, in an IP network, a ping is a network took that allows you to determine if a host is available on the network or not. It uses ICMP echo packets (https://tools.ietf.org/html/rfc792) to do the deed.
When somebody says ping a mobile on the network, what he really implies is to determine if where (what cell it is connected to) that mobile is in the network. So, this can mean the mobile is trigger to do a forced location update (LU). The mobile then reports itself into the network with its latest information.