I know you can convert the particles into a mesh but you loose the animation data of the particles when you do that.
Found a way here Convert particle system to animated meshes
This solution is not perfect. The euler rotation of the particles is not captured perfectly and the workflow to export to unreal is a bit tricky and "crashy".
When you export to fbx make sure you only select a single mesh as more than a couple might crash unreal engine on import. But the interesting thing is that there are multiple animations stored. So you can duplicate the mesh in unreal and select a different animation to create a flock of birds for example. It's no where near as good as the blender particle animation but good enough for a variety of applications.
Hopefully someone else can provide a better solution.