I’ve always been adamant about not running a character as a DM. I’ve been part of some bad groups where the DM ran a character and made the star of the show. In the next campaign I’m running my group wants me to run a Cleric for them. What are your thoughts on the Dungeon Master running a character?

Be careful.  Be very, very careful.  If the NPC travels with the party most or all of the time--which is usually a very bad idea--keep it out of the spotlight at all costs. 

I would make it to where your npc if you decide to have one, would have their own life and object to going on certain adventures because they have their own thing to deal with, swap your npc campaign character so the party does not rely on one for guidance or whatever they need out of them. If your hurting for a healer, try adding in some unconventional healer npcs (otherwise you run the risk of an army of clerics), or add in some potion drops and make them be more tactful with that.

A group I have played with for years decided to use the optional rule when we use inspiration we change who dms. Basically it means we all at some time have had to npc our characters, and then at some random time suddenly they become pcs again. 

To handle this we make sure when we npc our character we make sure to stay in character and make mistakes, just like our characters would make. Secondly when we dm we don't give out characters any special tresure. If you character is the only one thatbiaes a shield no magical shields. The big one is sharing the stage light, which hasn't been a issue.

For you I would suggest the above. Play your npc character like a character, I would not suggest the group leader, but let him cast useful spells when you think he would without meta gameing, amd be useful again no meta ganeing. Let him make mistakes, he wants to go left in a dungeon even if left leads to a dead in or a trap. Or he is hell bent on punching out the bartender even when you know the bartender is a retire 20th level monk, drunken style. Use him to make your storyline flow. If the story gets bogged down cause the players are lost, have your cleric suggest something, just keep in character.

For gear be random and make sure he gets last dibs, once all the players have a magic weapon then it's your turn. 

Good luck, but I don't think it's a big deal as long as you remember your character is second fiddle to the players, maybe someday one of them will run and it will be your turn to shine.

Personally I'd like to throw out the mandatory "DMPCs are pretty much always a terrible idea" warning.

My recommendation is let them take a Skilled Hireling, pay it 2GP per day, and have it possess the Healer feat, but no actual spellcasting.  

Seriously if the party just doesn't want a cleric but is concerned about healing, one of them should just be taking the Healer feat regardless, it'll do the job.  There's absolutely zero Need in 5e to have a Cleric or Druid per se, Healer feat + short rests when needed does the job just fine.

As to the DM running a character?  You already run hundreds of them.  You don't need one of them to be a permanent party member.  Have a Human NPC Healer at 2GP per day, they'll find the first chance to rid themselves of your services they can, which is for the best.  You're not there to participate in combat, or to guide them, or to have any special connections to Anything, you're just following them around and healing them when they need healing, which is what they're paying you to do.  Oh and that's 2GP per day... plus expenses.  Healer's Kits don't replace themselves after all :-)

First of all, make sure that this guy doesn't solve puzzles or give input unless asked. That's player work. It's okay to participate in combat, however, as it's still okay if you are just fighting and acting as an occasional help if asked. The most important thing to remember is that the main focus should always be on the players. 

If it helps the Cleric I made is a Kobold. He has a 7 strength and 10 Intelligence. He’s lawful evil and basically only follows whoever is the strongest and won’t kill him. He has a 16 wisdom to know this and a 13 charisma just to persuade people to let him live. He was made to be a servant of the party. Also when they first meet him he is a slave to a gnome that hires the group and during the first combat he kills the gnome and steals his gear.

He fights with a dagger because it’s the only finesse weapon a cleric can use at level 1.

Just have the pc you are running be more of a tag along, he doesn't weigh too heavily into party decisions and he isn't the crux of any plot advancement, he is there for fairer combat and to help with small stuff.

The only issue I see if trying to not meta game against yourself 

During reading this I was thinking it might be interesting if the cleric wasn't actually a physical being, maybe they stumble upon a magic item that holds the spirit of a priest and they can invoke the spirit to have it cast spells for them, but maybe it requires some sort of tribute to be given. Gives them access to a healer, without him taking items in the traditional sense, plus gives you a nice narration device if you need it.

Quote from Madclergy >>

During reading this I was thinking it might be interesting if the cleric wasn't actually a physical being, maybe they stumble upon a magic item that holds the spirit of a priest and they can invoke the spirit to have it cast spells for them, but maybe it requires some sort of tribute to be given. Gives them access to a healer, without him taking items in the traditional sense, plus gives you a nice narration device if you need it.

That could work.  Thanks.

I have a group that has never played before so they don't know about party balance. I didn't feel like railroading them into any classes so they ended up with no solid healer and no solid tank. I'm planning to drop a paladin on them to make their lvl 1 lives a little easier.