Here is my experience I had brown algae as well I would like to mention few things I learnt
1. Brown algae grows more in alkaline conditions pH around 7.0, If you lower your pH you will have same type of algae but with green colour.
2. The one of the root causes of Diatom algae (brown algae) is Excess silicates, which is from the rocks that are not cleaned well, or by using rocks that is found in your surroundings.
3. Low Light and in sufficient CO2 will encourage brown algae.
4. They will kill your plants by covering their leaves especially broad leaf plants, I lost 4-5 of chain swords.
5. Don't overfeed your fish even if you under feed it is okay.
SOLUTIONS I TRIED:
1. Some suggest to wait sure it will go away with time but it will kill 60-70% of your plants as well.
2. I started setting pH to 6.5 the brown algae growth became slow or nil.
3. I have never tried Amano shrimp but what I read was they are not so much interested in brown algae they are excellent for hair algae and all.
4. I have some snails they do eat brown algae but very slow and too much of snails look awful in tank.
5. THE SOLUTION WHICH WORKED FOR ME: Otocinclus they are bit costly but they like brown algae more than anything in 4-5 days they cleaned my glass for next few days they cleaned me rocks now they are cleaning my leaves. They are bit costly but they are effective I have 5 of them in my 29G tank. but they are sensitive till in first 1-2 days once they get going they are hardy, all my otos has big round tummy by eating all day long.