There are a lot of questions so I'll try to answer each one individually:
'you'll leave the UK at the end of your visit' - is a letter from his
employer stating that he is due to go back into work after our holiday
No. It isn't. People often extend leaves quit their jobs while on vacation, etc. So this letter is not that strong of evidence. Strong evidence would be family ties, a business that he has to run, property he has to manage, etc.
A letter of employment however, stating your partner's position, how long he has been working there, the amount of his salary does show proof of ties.
A letter from the office stating that he is due to get back to work would only work if the office was sponsoring or paying for part of his trip, in which case (in addition to the letter you mentioned) another would be required mentioning the kind of support provided.
We don't want to book a flight before his visa is approved, just in case.
As well you shouldn't. In most visa applications, only a flight booking is required, but some consulates require a full reservation. You may want to check by calling the local office; and @GayotFow might be able to answer a bit more authoritatively on this point.
'you're able to support yourself and any dependents for the duration
of your trip' - I understand that this should be shown with bank
statements. We share our bank account here as he is not from Bali and
can therefore not open a bank account in Bali as he doesn't have a
Bali resident card(he can only open a bank account in West Java, where
he is from).
So, can we show my bank statements?
'you're able to pay for your return or onward journey and any other
costs relating to your visit' - I suppose this relates to the bank
statement question above.
These two are related. Keep in mind that each applicant is judged on their own individual circumstances. In your case, effectively you are the sponsor for your partner on this trip - in that all the finances are in your name. I would consider drafting an affidavit of support mentioning your details, and your partner's and that you are willing to assume the costs of your partner's trip.
Finally, should we provide a letter stating that we are travelling
together and that we will be visiting my family and that we are both
working in Bali (I have a KITAS) so we are obviously going to come
back and we can afford the trip?
This letter would not help your application, I would personally not include it as it cannot provide evidence sufficient to the nature and purpose of your trip. Just because you have KITAS doesn't mean your partner will be coming back.
We plan on spending a couple of days in London so we can see my
brother and my friends and we will be staying with my brother, before
heading down south to stay with my family there.
My parents have a house there and I use that address as my home
address, so would that suffice as proof as to where he is staying?
Ah here is something good. You can have your parents submit a letter stating that they are aware that you are arriving with your partner (along with his details), and that they agree to host you both at their residence (provide proof of residence such as a deed letter, utility payments in your parent's name, tax receipts, etc.) and additionally if they are able to - they may want to add that they are also willing to cover the expenses of your trip.
Now, given all the above I have to say your application is of high risk - as it is very easy for you and your partner to elope to the UK, get married and for him to be a de-facto immigrant. There is of course, nothing wrong with you marrying whomever you choose its just that the type of visa and the kind of scrutiny given to those applications is different than just hey we are going for holiday together.