How to gather life-history traits data on bird species?
Have you tried the Ecological Data Wiki? It's an NSF-funded repository of links to ecological databases and datasets:

Main page:
http://ecologicaldata.org

Find data tab, refined to Taxon=Birds, Ecological level=Species:
https://ecologicaldata.org/search?f[0]=taxonomy_vocabulary_2%253Aname%3ABirds&amp;f[1]=taxonomy_vocabulary_6%253Aname%3ASpecies

The 'Avian body size and life history' dataset on the above page looks relevant to your search.