How is "advices" used incorrectly in the following sentence?

Advice is a non-countable noun. You can give advice, or some advice, or a lot of advice, or a little advice, or no advice, or a piece of advice, but not "an advice".

However you can offer suggestions.

I would revise the sentence like this:

"If you have any advice you would like to provide, please feel free to give it."

Or

"If you have any suggestions you would like to offer, please feel free to state them"

so "advice" is correct but "advices" is incorrect because I shouldn't add an s. My question is advice is only singular then not plural? Thanks!

It is neither singular nor plural. It is non-countable. You can have some advice or no advice but not an advice or some advices.

You haven't provided enough context, the problem we always have with EFL students. If the sentence you have provided is from a source even as recent as the late 19th or early 20th century, the usage is correct. If the sentence was written within, roughly, the last century, it is a quixotic use of a now outmoded usage. The plural advices was used well into the 19th century to mean more than one piece of advice given by more than one person. That was, however, even then, a not very common usage. It was more commonly used to mean news or information. So, for example, a newspaper in England in the 1750s reporting on the course of the Seven Years War might have written: The advices of our correspondents in Vienna suggest that the Prussian advance through Lustatia found the Austrians completely unprepared. When advices was commonly used, it was most common used in that way--to mean news or information.

So my understanding is "advice" is non-countable word which means I cannot have more than one advice? I am a little confused because you mentioned that back in the late 19th century and early 20th century, people did use the word "advices", so what about now? The context has changed?

"She gave me few advices but I did not listen" So...the word "advices" in this sentence is incorrectly used because "advice" is not countable, correct?
What about
"she gave me some advices on how to sew" in this sentence "advices" would still be incorrectly used?

Where as...
"She gave me the advice to eat a small meal before working out"
"The advice I have for you is not to procrastinate"
The word "advice" in these two sentences is used correctly because according to what you have explained, you can give advice or have advice but cannot have advices. Is that correct? Thank You so much for your information and help!

I am confused because according to Dictionary.com
http://dictionary.reference.com/browse/advices

The word "advices" seem to exist
Can someone please explain? Thank You!

The word has fallen out of use. People no longer use the word advices. The context has nothing to do with it now. I asked for context because you didn't give enough text to make it clear what the source was for the sentence, and i'm not going to spend my time searching for your sources.

Until the 19th century, "advices" was used in certain contexts. Although it was falling out of use, it was still to be seen in the early 20th century. I asked for more context from you so that i might judge if it had been properly used in the source from which you got your sentence.

People writing today should probably not use the word "advices" because contemporary usage considers advice to be both singular and plural. Mr. Jones gave me some good advice. I got good advice from several people, but the four or five pieces of advice from Mr. Jones were the most helpful.

You didn't notice, but your search at Dictionary-dot-com redirected you to the word advice. The definitions you saw there were for the word advice, not advices. The word advices does exist, but it is outmoded--it is no longer in use.

Thank You for the valuable information!