You are right - there are various problems with the construction of that sentence. A fluent English speaker would find it confusing and/or awkward.
(In context, I can guess that the intended meaning is, "I know that there is a lot of furniture in my flat". But without the context you gave, I would struggle to understand the original sentence.)
"I know that the furniture of my flat is much", and "I know that the furniture of my flat is a lot", are semantically unclear. This is partly because of word order, and partly because of the various possible idiomatic uses of 'much', and 'a lot'.
In English, a word or phrase that describes the quantity or amount of a thing, is placed before the noun. This is called a quantifier. For example: 'two bits of furniture', 'a lot of furniture', 'many chairs'. http://www.myenglishpages.com/site_php_files/grammar-lesson-quantifiers.php
An adjective (or adjectival phrase) describes the quality of a thing, and goes after '[noun phrase] is'. For example: 'the furniture of my flat is beautiful', 'the furniture is plentiful', 'the furniture is grandiose'.
So, a native English speaker would understand 'much' at the end of the sentence to be describing the quality (rather than than the quantity) of the furniture. She might wonder whether part of a common colloquial phrase had been left out by mistake. Should it actually say that the furniture is: 'too much'; 'a bit much'; or 'much of a muchness'?
"the furniture of my flat is a lot" could also be misunderstood without context. Is it identifying all of the furniture as a single 'lot' for sale in an auction, for example?
[Also, "my flat's furniture", and "the furniture in my flat", are more natural English expressions that "the furniture of my flat"]