Yes, depending on which text app you're using. For example, with Verizon Messages, you long-press an e-mail string, get a pop-up and choose Delete Conversation, then place check-marks to the left of all the e-mail strings. Once you tap the trash can at the top of the screen, they're all deleted.
If you aren't using Verizon Messages, specifics could be provided once we know which phone/text app you're using.
Verizon needs to change the apps so that you can choose all message at once, with one click and delete. Checking each individual convo or message is way too time consuming.
We want to make sure you have every resource to manage your messages the way in which you prefer. Deleting multiple entire conversations can be done when you log in to My Verizon from a computer. The instructions highlighting this can be found here: http://spr.ly/66061ddhY
Does this help?