Do birds require cilia for left/right symmetry during their embryological stages?
Here is a paper that talks about left-right patterning across bilateral organisms, discussing both Xenopus (frog) and chicken. 

It looks like it may be hard to generalize, but the answer appears to be "yes" for Xenopus and "no" for chicken (see e.g. Figure 2, and text immediately following). 

However, it looks like the question of what exactly is going on in chicken is not well understood, according to this other paper. Chickens do have lethal ciliopathy mutants homologous to mutants causing left-right defects in other organisms, but these mutants appear to have normal left-right asymmetry development in chicken. 

It is also not clear that the requirement of motile cilia for left-right asymmetry is generalizable within clades though, as pigs have apparently also lost the dependence on cilia for L-R, whereas mice and humans do require cilia for L-R. It appears that pig and chicken have dispensed with cilia by the same histological mechanism (see image below, Figure 7 of first paper).

I do not know whether the mechanism has been investigated in other birds.

Hope that helps.