Aurora Store is great but it can be a little …flakey
Probably, if you look again, the install button will be there 
Yes, this a known problem (at least known by me ). This ofen happens when you have just installed Aurora. My workaround is to do one or more of the following until it works:
- In Aurora Settings > Downloads
- Set Active downloads to a bigger number - 7 or 9 work for me
- Set Download strategy to “parallel download (splits)”
- In Settings > Apps and notfications > Aurora Store
- Check it has all permissions granted (including Advanced > Install unkown apps)
- Clear cache and storage (which means you will have to repeat step 1.
- Reboot the phone
Repeat any or all of the above until you press install, and it starts to download.
Also check out this post and subsequent posts in that thread.
I know this is all a bit of a faff, but it’s great once it starts working Good luck!