Good morning and thank you for the questions!  

Congratulations on establishing your flower garden and especially your recognition for the need of adding compost.  As you add compost (organic material) to your garden you will greatly increase the soil's ability to retain water, which means a more constant supply of available moisture for your flowers.  Compost will also reduce the possibility of soil compaction, which will encourage better flower root development.  It is important to realize that often times compost per se may have rather little nutrient content.  In other words, adding compost will not necessarily eliminate your need to add fertilizer.  My suggestion:  after you add your compost and mix it in, take a soil sample and have it analyzed to determine how much fertilizer, if any, should also be added.  Soil testing can be done at the University of Minnesota.  See the following for information and instructions as to the submission of a soil sample:

http://soiltest.cfans.umn.edu/testing-services

Now to your specific questions:

1)  To begin with and since this will be a new garden, add about three to four inches of compost into the top foot or so of soil.  Work it in well.  Your garden will be 160 square feet.  This means that you will need a total of about 40 cubic feet of compost.  This works out to about 1.5 cubic yards of compost.  Use this as a guide when obtaining your compost.

2).  With respect to the type of compost, consider making your own.  While this will not be possible this season, it may be something for you to consider in subsequent years.  The following University of Minnesota publication will give you further information on both of these points as well as other things you should consider (be sure to check out the various pull-down menus):

https://extension.umn.edu/how-manage-soil-and-nutrients-home-gardens/amending-soils-perennial-beds#compost-1414061

3).  While I am not totally familiar with what might be available this current season in Minneapolis, check out the following for sources of compost:

http://www.startribune.com/dollars-and-sense-where-to-go-for-free-wood-chips-and-compost/94662529/

As a Master Gardener I cannot advocate for any specific commercial brand of compost.  However, cow manure/compost is sold at Menards in 40 pound bags.  This might be a possibility.  I don't know what this means in terms of volume so you would need to determine that.  Check out other types of commercial compost.  The exact type will not be critical.

Please get back to us if you have further questions.  Good Luck!!