Learn English – How was your weekend

Yes, it both "sounds wrong" to a native speaker, and it doesn't make sense.

The phrase "[person] has been to [place]" simply means the person was present in the place at least once. It contains no information or implications about when they were there, for how long, or why. "has/have been to" is completely without duration. Asking "how long" makes no sense.

The question "Have you been to [place]?" is a question with a "yes" or "no" answer. Are you asking how long ago the person visited? Are you asking how long they stayed in the place? In either case, one would ask those questions instead.

I'm not a native speaker but I googled and found the word flextime.

Judging by the Wikipedia article, you can say

I work flexible hours.

or

I have a flexible working schedule.

If you want to somehow use the words "weekends" and "holidays" in the sentence, you might say

I have no fixed weekends and holidays, and my working schedule is flexible. It is me who decides when to have a weekend or a holiday.

If you just say

I have no fixed weekends and holidays.

... the listener might misinterpret that as "I have a very demanding job, and cannot be sure that I'll be off-work on a particular weekend or holiday".

If you have no boss, that is, if you are self-employed, you might say just that to explain why you have no rigid work schedule:

I am self-employed, thus my working schedule is free and has no fixed weekends or holidays.

I'm a freelancer, thus the terms "weekends" and "holidays" do not apply to my work routine. I work when I need to, and I take rest when I feel like it.