Is there an alternative metric to GDP that measures a country's assets rather than flows? The Gross domestic product measures the value of all final goods and services produced in a period.

This has some limitations.  For example, if a car hits a lightpost and both need to be repaired and some parts replaced, that contributes to the GDP, even though at the end we're in roughly the same situation as before and the reparation process has used resources (labour and material) that might have been used elsewhere.  From Wikipedia:


  The UK's Natural Capital Committee highlighted the shortcomings of GDP in its advice to the UK Government in 2013, pointing out that GDP "focusses on flows, not stocks. As a result an economy can run down its assets yet, at the same time, record high levels of GDP growth, until a point is reached where the depleted assets act as a check on future growth". They then went on to say that "it is apparent that the recorded GDP growth rate overstates the sustainable growth rate. Broader measures of wellbeing and wealth are needed for this and there is a danger that short-term decisions based solely on what is currently measured by national accounts may prove to be costly in the long-term".


I'm aware of numerous alternative measures focussing well-being, such as the Human Development Index,Gross National Happiness, and the Happy Planet Index.  They don't really measure either wealth or well-being (the latter may be impossible to measure), and their exact definition is somewhat arbitrary.

Is there any reasonably well-established alternative to GDP that measures the total value of the stocks of a country?  Wikipedia has a financial assets list, but it relates only to households (and on this list, Greece is almost twice as wealthy as Norway, which is so vastly against expectations that I wonder if the definition is useful).  I can reasonably well estimate the value of my own assets (except for the value of my education/skills, which is harder to quantify).  Is there any metric that is used to estimate the value of all assets in a nation: infrastructure, real estate, machines, goods, farmland, but also education, human capital, unmined natural resources, etc.?
You are correct in pointing out the flaws of GDP. But honestly, it's the best we have came up with; measuring the stock of wealth is just impossible. 

You say you can estimate the value of your own assets, and of course it seems that way. We all feel that way, until we actually try. How much is your cellphone worth? Easy to know, go to ebay and look for similar phones in similar conditions and you get a price for that phone, right? Why don't we do that for all the country's cellphones? Well, because if we put all the cellphones in the market prices would drop down dramatically. Now, we're not obviously sending all the cellphones to the market, we just want to know how much its value is, but the point is that in order to have an estimation, we have to make assumptions regarding the market. The value of one cellphone is easy to calculate because it doesn't really affect the market. 

Additionally, who says that you have to sell it in your local market? Why don't you offer it in Australia or Japan or Algeria or wherever the price is higher? And why not sell it another day when the price is up? The same goes for your car, house, computer, clothes, books, etc.

Think now of your financial assets. You can know that, right? All one needs to do is see what the bank says, and it says that my investment portfolio is worth \$100.... at least today... and exactly at the time I checked. But remember: the value of any financial portfolio is going up and down with high volatility even in the same day. Now try to figure out the value of the financial assets of all the country. Well, you can do that. But again: just today, and just at the time you checked. 

Even though it doesn't seem like it, the same goes for goods. Take oil. Say that there is an oil reserve with x millions of barrels just waiting to be extracted and sent out to the market. How much is the value of that reserve? It depends on when you ask, whom you ask to, and who else is asking the same question (other sellers). What about gold? silver? copper? coal? wood? You can estimate a value in a given time, but that can be very different in another time.

What about land? Well, if I sow corn it will give me a given amount, but if I sow rice it will yield a different amount. Besides, would it be the same if my neighbor sows corn and I sow rice than if we both sow the same (competition)? What if I want to use it to generate electricity instead of growing food? Or what if I use it for livestock? What if I sell it? What if we all decide to do the same thing at the same time? Or what if we decide to do completely different things? Indeed to value farm land, you have to assume what use will it have.

Infrastructure is even more complicated. How much is a railroad valued? And what does value even mean in this context? There is no secondary market for railroads is there? There are opportunity costs, though. And we have the construction value too. But the we would have to make assumptions on its depreciation, and say how much of the revenue of the country is due to this specific segment of the railroad. To estimate this, one has to say how much the country would loss was the railroad not there (which is a fictitious value). What about parks?

Don't even get me started on natural resources (rivers, lakes, coast, jungles, biodiversity, etc). But even then, those are the easy ones. We still have left education, experience, skills and the like. But this post is long already, the point has been made and now I have a headache for thinking all this. 

Indeed, there are many serious and very clever attempts to make estimations of these. But they are used to answer very specific questions. GDP, on the other hand is easy: just sum all the sells of goods and services. We (economists) don't like it very much either, but that's all we have. Just try to accept it, and don't take it to seriously.