You don't need to install ESXi to any one place or another. If it supports booting from a particular media type or location then it's ok to install it to that location. ESXi is quite particular about only booting and working properly with supported hardware (as per its HCL) used in supported configurations; if it doesn't like something you're trying to do, it will be sure to let you know...
Having said that, if my choices included a local install on a flash card then I'd always do that for simplicity's sake on a production server. One less complication to troubleshoot if you have any problems and just need to get the damn production network going again at 3am in the morning while your boss is yelling down the phone at you, you know?
Edit...
As for your comment about the storage types, my apologies - when I saw 'Dell Virtual Disk' I was thinking of the volumes that get created by a Dell SAN, but if its local disks then that's going to be a RAID array created by a PERC raid controller I'd imagine. If both these locations are local storage then there's even less reason to worry in terms of 'will it work...?'
As for best practice - if you're likely to be building small 'single server' virtual servers then it makes sense to reserve the local hard disk storage, the virtual disk, as a container for the virtual guests themselves and install ESXi onto a flash card. It keeps things tidy and ensures you can easily upgrade ESXi (some upgrades in the past have required changes to the disk layout) without having to touch the disks holding the virtual machines, which makes a certain amount of sense as I'm sure you can imagine.
Deleting the ESXi install partitons with a Ubuntu Live CD will be just fine, by the way. While ESXi isn't a Linux clone, it handles disk partitions in a standard enough method to allow you to inspect and delete them like this.