Will "bakelite" handles on flatware get yucky over time?

Yup. Yucky if you are referring to becoming discolored and cracked. They still work, until they crack and fall apart and all of ours did after several years. Maybe you should go with stainless steel and a good over mitt for cook ware and I doubt the spoon will get so hot at the handle it would burn you! Just looked at the link:

(Lambert espresso spoon, A charming addition to small serving dishes as well as to your sugar bowl or coffee cup. Brushed stainless steel with bakelite handle.
Price: $12.75)

It is up to you, I wouldn’t go this way and I think it’s the dishwasher that ruins the bakelite. Good luck!