I have LUKS disk encryption on my linux installation. I would like to encrypt files on a usb by using Veracrypt. Will having Veracrypt installed on top of my LUKS installation have any bad effects? Will it work properly? Will both the standard volume and hidden volume options work properly? And lastly is doing this secure and private? Or should I just use LUKS to encrypt usb flash drives?
You can encrypt your USB drives using Veracrypt for as long as you install Veracrypt software on your Linux (so you would be able to access them from Linux).
You are using LUKS to encrypt partition(s) on your hard drive but once you boot-up the system, you can work on it just as it was not encrypted and use Veracrypt.
You need to distinguish the difference between the system/partition encryption and file/container/folder encryption. First is LUKS (I know, you can use Veracrypt to do it, but since you have your system encrypted by LUKS, there is no point to encrypt it again with Veracrypt), the second is Veracrypt - very good for file/container/folder encryption on a host system or portable drives. It is important to remember, that you would need to install Veracrypt OR put portable package along with encrypted files on any system that would need to access your portable (for instance USB) drives. You would also need admin rights on these systems to use portable package. You can copy the encrypted containers wherever you like.
LUKS has nothing to do with your USB drives, Veracrypt has, you can encrypt them with any Linux compatible software you like. You can even encrypt files you keep in the cloud to protect them from being viewed by unauthorized individuals (in case of security breach) or personnel of your cloud provider.
Both types of volumes will work fine and yes, it is safe.