So this one time, I was trying to solve a hard problem and my boss who is a native English speaker said "Don't flail, give to X he knows how to solve this."
Ever since then whenever someone gives me a hard problem to solve, I pretty much always say "Let me Flail a bit then I will go ask someone for help".
Is that a valid way to use that word?
flail (v): 1.1 Flounder; struggle uselessly.
Your boss initially used "flail" to tell you that, if you have no idea how to do something, you should hand it off to someone else. Otherwise you're just wasting time. It's not a good idea to use "flail" to describe your own efforts, as it suggests you will simply struggle and achieve no useful result.
Instead, use a more positive term that implies that, even if you do not make progress, you still are putting in a meaningful effort.
Let me work on the problem for a bit (before I ask someone else for help.)
Let me wrestle with the problem for a bit.
Let me plug away on the problem for a bit.
Let me sweat over the problem for a bit.
along with various others. These all imply you are making good use of the time, even if you may eventually fail to achieve the desired result.
As I mentioned you can use "flail", if you are speaking with a kind of ironic "false modesty", knowing that your effort will succeed, but wanting to sound humble.
For example, suppose I am an excellent artist. A friend asks me to paint a portrait of her relative. I know I will do a good job, but in order not to sound boastful, I might say:
Well, I suppose I can flail about with my paints and brushes, and hopefully the picture won't be complete rubbish.
Here's how Merriam-Webster defines flail:
intransitive verb
: to move, swing, or beat like a flail
// arms flailing in the water
Your boss is using this word metaphorically, as @DavidSiegel points out. I think he's telling you to stop vacillating or hesitating about what to do next. Flailing is a negative action - when you do this you are wasting time by hemming and hawing and not being sure what to do next. You probably should not use flail the way you do ("Let me flail...") - it does not mean "trying to solve a problem without knowing how to solve it". "Let me flail a bit" sounds like "Let me panic and waste time not knowing what I'm doing for a while". Instead, I would suggest saying something like:
Let me try working on this problem myself for a while (before I go ask someone else for help).
Literally, "flail" means to strike with a flail, a large and somewhat awkward whip, or an implement for threshing grain. It is rarely used in this sense any more. Metaphorically, "flail" means to go back and forth or to move at random, or try things at random, without fully knowing what one is doing, to move as if blind, drunk, or confused. This, as I understand it, comes from the poorly controlled movements often experienced when using a literal flail.
I believe that the form was formerly most often "flail about" as in:
Don't flail about when you don't know the system, ask for help.
And the use of "flail" without "about" is a shortening or elision, with "about" implied.
"Flail" can also be used to mean to strike hard but somewhat at random, as if with a flail:
The opposition flailed Mayor Jones for not getting federal approval before starting the project.
My boss flailed me for trying to do the project I didn't understand without asking for help.
This is not the sense in which your boss seems to be using the word, however.
