You will not need to apply for planning permission to paint or maintain the external walls of your flat or maisonette. However in some areas these rights have been removed (by way of what is known as an article 4 direction).
If you are a leaseholder, you may first need to get permission from your landlord, freeholder or management company.
If your flat is a listed building you will need listed building consent, unless it is repainting in the existing colour, and you should contact your local planning authority to determine this.
Works to a listed building that affect its special historic character without consent is a criminal offence.