My significant other has an expired visa which allowed him to enter the US legally. However, this was almost two years ago this summer.
Would they be allowed to travel on vacation to another state via airplane?
Travel between US states never requires presenting a visa. When boarding the plane, you will be required to present a valid, current ID, but they won't check your visa status then.
Only if you raise suspicion in some manner (trying to carry knives on board or something), is anyone likely to inquire about visa status.
One exception would be that if you end up driving north, away from the Mexican border, you may pass a US Border interior checkpoint, where your visa status may be checked.
For example, if you were to fly from Denver, Colorado, to McAllen, Texas, then drive to Houston, your visa status could be checked on the drive.
But it doesn't sound like you're planning a road trip where this would apply.