If the trend in the burndown chart in fluctuating like Up, Stagnant, Down and 0 at the end of sprint. What does this indicate?

More importantly, did the team achieve the Sprint Goal and deliver any working functionality? 

As for the burndown....

If you're above the trend line typically it it means the team is behind the forecasted work

Even with the trendline would indicate on track

Below the trendline would show they're ahead

Neither of these things are necessarily bad depending on the context in which it's being reviewed. Remember data without context can be misleading. 

Regardless of what it looks like, are the team able to explain their burndown profile?

More importantly, did the team achieve the Sprint Goal and deliver any working functionality? 

@Tony - Yes.

Here, may I consider the pattern on the Burndown chart to judge the MATURITY of my Scrum Team? Is it a good metric to judge that?

Is it possible that a matured team's burndown chart will go along with TrendLine rather than fluctuating above / below?

I personally don't believe it's a good metric to judge team maturity. A mature team can still have ebbs and flows on the burn down. If that's a tool they're choosing to use then it's what they do with this information that matters. 

Is it possible that a matured team's burndown chart will go along with TrendLine rather than fluctuating above / below?

Consider you are a perfect driver and have to drive from Point A to Point B. Google maps shows the ideal time that will take you. But on your way you discover road blocks, constructions, accident or a bad weather due to which you are redirected to several other routes. Let say at the end you finally reach Point B. But does it make you an imperfect driver ? 

In addition to the above points you should also look at how metrics are being generated and whether the metrics accurately reflect the team's progress.

For example: I've seen many Development Teams that, though the team remains confident that they are on track for the Sprint Goal on an almost daily basis, the actual work remaining remains above the trend line as it is being captured. They run into impediments (what you described as road blocks, constructions, accident or a bad weather), but are able to quickly resolve issues and consistently complete their Sprint Goal, producing a potentially releasable increment of their product at the end of each Sprint (sometimes sooner). When asking the team "are these metrics useful to you? are you able to interpret them? Are they an accurate reflection of your progress during each Sprint?," responses would range from "those are just something that (Scrum Master, Product Owner) looks at" or worse "those are reported to (management, stakeholders) and only cause us trouble." If the Development Team doesn't find the metric useful/representative, then don't rule out the root cause being the metric itself and how it is generated.

I'm in agreement with Lauren's response when it comes to tools like a Burndown. It can quickly become a management driven micromanagement tool if it's not owned by the team. 

Sometimes challenging the team to find their own way of creating the same transparency could be better because it increases the accountability and sustainability of the practice. I've worked with a team that just used a red / green indicator. If someone felt the Sprint was endanger they'd flip it red and the team would come together to inspect the challenge and determine what needing done to go back to green. 

Or, you start red and set goals within the Sprint that would be met in order to flip to green. 

Point being, if the burndown isn't getting the engagement and ownership from the team perhaps there's other creative ways to accomplish the goal. 

I would add to this conversation that using output-related metrics to assess Agile maturity is a poor approach.

It may help with assessing how productive a team might be, but it does nothing in regards to measuring customer satisfaction or a team's ability to pivot.