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When I express myself on paper or verbally my goal is clarity.

Putting to one side the parts of speech which may be involved, the OP is asking whether there is ambiguity (and how it might be made clear).

The two phrases under discussion - a dark blue necktie and a black polka dot dress have a clear, implied sense to me as British English speaker:

the necktie is dark blue in colour and the dress has black polka dots. Any other interpretation can be given easily by reordering the words, for example:

a blue dark necktie; a polka dot black dress.

The oddness of these two versions suggests that interpretations other than the (obvious) implied sense are wrong. In the first phrase 'dark' must qualify 'blue' - how can a blue necktie be dark except because its blue colour is a dark blue? The second version of the polka dot dress makes clear that this phrase is deliberately ambiguous. Only one colour is given but, clearly, another colour should be included since the dress background and the polka dots cannot both be black.

Instead of using word order - the idiomatic approach to conveying meaning - there is always punctuation:

a dark, blue necktie; a black, polka dot dress (making clear that the polka dots are a colour other than black).

Putting to one side the parts of speech which may be involved, the OP is asking whether there is ambiguity (and how it might be made clear).

The two phrases under discussion - a dark blue necktie and a black polka dot dress have a clear, implied sense to me as British English speaker:

the necktie is dark blue in colour and the dress has black polka dots. Any other interpretation can be given easily by reordering the words, for example:

a blue dark necktie; a polka dot black dress.

The oddness of these two versions suggests that interpretations other than the (obvious) implied sense are wrong. In the first phrase 'dark' must qualify 'blue' - how can a blue necktie be dark except because its blue colour is a dark blue? The second version of the polka dot dress makes clear that this phrase is deliberately ambiguous. Only one colour is given but, clearly, another colour should be included since the dress background and the polka dots cannot both be black.

Instead of using word order - the idiomatic approach to conveying meaning - there is always punctuation:

a dark, blue necktie; a black, polka dot dress (making clear that the polka dots are a colour other than black).

When I express myself on paper or verbally my goal is clarity.

Putting to one side the parts of speech which may be involved, the OP is asking whether there is ambiguity (and how it might be made clear).

The two phrases under discussion - a dark blue necktie and black polka dot dress have a clear, implied sense to me as British English speaker:

the necktie is dark blue in colour and the dress has black polka dots. Any other interpretation can be given easily by reordering the words:

a blue dark necktie; a polka dot black dress.

The oddness of these two versions suggests that interpretations other than the (obvious) implied sense are wrong. In the first phrase 'dark' must qualify 'blue' - how can a blue necktie be dark except because its blue colour is a dark blue? The second version of the polka dot dress makes clear that this phrase is deliberately ambiguous. Only one colour is given but, clearly, another colour should be included since the dress background and the polka dots cannot both be black.

Instead of using word order - the idiomatic approach to conveying meaning - there is always punctuation:

a dark, blue necktie (making it clear that 'dark' on its own in this context, is meaningless);  a black, polka dot dress (making clear that the polka dots are a colour other than black).

When I express myself on paper or verbally my goal is clarity.

Putting to one side the parts of speech which may be involved, the OP is asking whether there is ambiguity (and how it might be made clear).

The two phrases under discussion - a dark blue necktie and a black polka dot dress have a clear, implied sense to me as British English speaker:

the necktie is dark blue in colour and the dress has black polka dots. Any other interpretation can be given easily by reordering the words, for example:

a blue dark necktie; a polka dot black dress.

The oddness of these two versions suggests that interpretations other than the (obvious) implied sense are wrong. In the first phrase 'dark' must qualify 'blue' - how can a blue necktie be dark except because its blue colour is a dark blue? The second version of the polka dot dress makes clear that this phrase is deliberately ambiguous. Only one colour is given but, clearly, another colour should be included since the dress background and the polka dots cannot both be black.

Instead of using word order - the idiomatic approach to conveying meaning - there is always punctuation:

a dark, blue necktie; a black, polka dot dress (making clear that the polka dots are a colour other than black).

OK. When I am expressing myself on paper or verbally my goal is clarity.

Putting to one side the parts of speech which may be involved, the OP is asking whether there is ambiguity (and how it might be made clear).

The two phrases under discussion - a dark blue necktie and black polka dot dress have a clear, implied sense to me as British English speaker:

the necktie is dark blue in colour and the dress has black polka dots. Any other interpretation can be given easily by reordering the words

A blue dark necktie, and a polka dot black dress.

The oddness of these two versions suggests that interpretations other than the (obvious) implied sense are wrong. In the first phrase 'dark' must qualify 'blue' - how can a blue necktie be dark except because its blue colour is a dark blue? The second version of the polka dot dress makes clear that this phrase is deliberately ambiguous. Only one colour is given but, clearly, another colour should be included since the dress background and the polka dots cannot both be black.

Instead of using word order - the idiomatic approach to conveying meaning - there is always punctuation:

A dark, blue necktie, A black, polka dot dress (making clear that the polka dots are a colour other than black).

When I express myself on paper or verbally my goal is clarity.

Putting to one side the parts of speech which may be involved, the OP is asking whether there is ambiguity (and how it might be made clear).

The two phrases under discussion - a dark blue necktie and black polka dot dress have a clear, implied sense to me as British English speaker:

the necktie is dark blue in colour and the dress has black polka dots. Any other interpretation can be given easily by reordering the words:

a blue dark necktie; a polka dot black dress.

The oddness of these two versions suggests that interpretations other than the (obvious) implied sense are wrong. In the first phrase 'dark' must qualify 'blue' - how can a blue necktie be dark except because its blue colour is a dark blue? The second version of the polka dot dress makes clear that this phrase is deliberately ambiguous. Only one colour is given but, clearly, another colour should be included since the dress background and the polka dots cannot both be black.

Instead of using word order - the idiomatic approach to conveying meaning - there is always punctuation:

a dark, blue necktie (making it clear that 'dark' on its own in this context, is meaningless); a black, polka dot dress (making clear that the polka dots are a colour other than black).