I recently notice that parts of my base board is starting to chip . I was not the one who originally painted the board, but it looks like its original coating was not paint. Is there a goo paint with a semi gloss or satin finish that will adhere to board?

My guess if the paint is failing that one of several things happened . They may have tried to paint with water based latex paint over previous oil based, which gives a poor result. Or there could be moisture or rot in the wood.

If the wood is good, scrape and sand thoroughly to get the loose stuff off and smooth any edges. Vacuum the dust off, wipe with a damp cloth (just damp enough to pick up the rest of the dust, not wet ). When clean and dry, Use a good primer (I like Killz) then paint. I like a gloss or semi-gloss latex paint for trim and a more flat eggshell finish for walls. Ask at the paint store what primer to use and explain the old paint is failing, and you aren't sure whether it's oil or water based.