Just a quick writeup on how I got my followers to prostitute themselves automatically. Note: I set this up using Skyrim SE, but it should work with Skyrim LE. You have to use that game's versions of Radiant Prostitution and EFF. Can't promise my custom patch will work with LE.

What you'll need:

Radiant Prostitution

EFF - Extensible Follower Framework, Or any other follower mod that makes your followers 'sandbox' on their own (i.e. Auto idle, wander around aimlessly interacting with objects)

Optional:

This patch for EFF will limit the followers Auto Idling to just 'Safe Areas' (Cities, towns, Inns, civil war camps, and orc strongholds). It also increases the distance from the player followers are allowed to sandbox, increasing the odds they will prostitute themselves. Make sure its listed after EFF in your mod load order:

 EFF_LimitedSandboxing.esp

Actual Tutorial:

- First make sure the MCM settings for EFF has 'Auto Idle' enabled. I also recommend disabling 'NPC Schedule' on Radiant Prostitution so your followers will work at any game hour instead of just 5 pm to 3 am:

-Next you will need to acquire a 'Sanctified Amulet of Dibella' for your prostitute follower to wear. Sadly that will consume their Amulet equipment slot. As far as I know the 'Working Clothes' feature will not work:

The normal way to get one of those amulets is to have the player do prostitution work for an Inn at least once. Then when asking to work again you'll get the dialog option to 'Find new talent'. The innkeeper will give you one of the amulets. If you are unwilling to prostitute your player you'll have to use console command cheats to acquire an amulet.

- Next simply get your follower to equip the amulet. Make sure they do not have any other amulets in their inventory as they have a habit of favoring other amulets. You should be good to go. Enjoy your wench companion!

Other Notes:

- Works for both female and male followers. I do not believe it will work for creature followers but I haven't tested that 

- Since the odds of a follower prostituting themselves is RNG based things can be a bit inconsistent. At times your follower will be constantly soliciting themselves. At other times they will behave like they are off duty or something. Expect uneven results.

- The followers get paid for prostituting themselves, but don't expect them to make you rich. I think the most I've seen one of my followers build up was about 1300 gold after serving many clients.

- Not sure how to toggle sexuality. Forgot to test that. EDIT: There does not appear to be a way to edit sexuality for Radiant Prostitution, so your prostitute followers will behave in a bisexual fashion no matter what their Sexlab sexuality has been set to.

- If you are going to be spending time doing busy work at a town/inn command your prostitute follower to 'Relax' via the EFF command wheel. That will cause them to wander much more freely. Increasing the odds they will search for clients. Command them to follow you again when you are ready to leave.

- If you have other followers you haven't setup as prostitutes your whore followers will sometimes solicit themselves to the non-whore followers. Not much that can done about that.