You can certainly boot from a USB if the PC you are booting to supports it. The problem you face is booting from an encrypted partition. This has been discussed on several occasions and the conclusion reached is that there is that you have a circular problem in that you need to decrypt the partition to boot it, but you need to boot to decrypt the partition. The work around is to leave an unencrypted /boot partition and encrypt the other partitions. Generally speaking, you should also (re)consider the necessity of encrypting stuff other than your /home partition. In other words, do you really care if someone sees a binary copy of bash that came from a repository for example?
I have heard one thing to keep in mind, but can't vouch for its viability, is that running Linux from a USB can wear out the USB stick faster because of the number of writes performed. Instead of using a flash drive, perhaps one of the small USB HDD's would be better.
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