I have been working on a prototype survival game project and recently added swimmable water but am in need of a few basic swimming animations, does anyone know of any free swimming animations that work with the default UE4 character rig?
Mixamo have some…I believe you get 20 free animations if you sign up now…not sure if that deal is still running but worth a look anyway. 
When you just need them as placehodler animations, you could also use the “prone” animations from the free animatione starter pack 
I just found this: https://gumroad/l/ParkSwimPack
Ignore the purchase, and they link to the free animations. They’re just Mixamo animations that have already been mapped to the UE4 skeleton which saves you the re-targeting step.
There’s basic mocap of all the swim styles in the usual mocap pack.
you can probably still pull it off this post
That said, backstroke and freestyle are rather simple to just make, being mostly linear.
If you have some experience with animation I would suggest you browse the mocap set, find the one you need, and parse it with my blender plugin. (://mosthostla/gamedev/bonebreaker)
You can then select 3 or 4 base key frames and create a clean cycle out of the base poses.
Simplifying the motion will result in a “not exceptional looking” animation, but if you are in first person it will work much better compared to the raw mocap data version…