I don't know why anyone wouldn't just use this:

https://www.amazon.com/Mityvac-MV8000-Automotive-Test-Bleeding/dp/B00265M9SS

Two man would be optimal and the cheapest method. I use the vacuum or pressure methods for flushing purposes. I assume you don’t have an air compressor so I own and use these tools for a one man no compressor purpose.

Vacuum

MV8000 Automotive Tune-up and Brake Bleeding Kit https://www.amazon.com/dp/B00265M9SS/ref=cm_sw_r_cp_api_i_soVQDbZJ9N047

Refill tank (used with two man or vacuum method)

Mityvac MVA6832 Clamp-On Auto-Refill Kit https://www.amazon.com/dp/B000K1KPK4/ref=cm_sw_r_cp_api_i_PvVQDbX1TZZBW

Pressure (with the correct adapter for the vehicle)

Motive Products, European Power Brake Bleeder, 0100, Hand Pump Pressure Tank with Adapter https://www.amazon.com/dp/B0002KM5L0/ref=cm_sw_r_cp_api_i_9rVQDb9QG3FXY

bottle top filters.
https://www.amazon.com/Whatman-10443421-Cellulose-
Regenerated-Bottletop/dp/B007GE9N3I/ref=sr_1_9?ie=UTF8&qid=1487620307&sr=8-9&keywords=whatman+filter
glass media bottle i use
https://www.amazon.com/PYREX-250mL-Round-Storage-Bottles/dp/B004XR5TIO/ref=sr_1_7?ie=UTF8&qid=1487620362&sr=8-7&keywords=glass+media+bottles
break bleeder
https://www.amazon.com/Mityvac-MV8000-Automotive-Test-Bleeding/dp/B00265M9SS/ref=sr_1_7?s=automotive&ie=UTF8&qid=1487620409&sr=1-7&keywords=brake+bleeder

Flushing isn't really the right word, all you're really doing is bleeding the brakes. You're just moving enough fluid through the system to introduce new fluid and remove the old. You can do it without a power/vacuum bleeder if you have someone to help you. I'm not sure if AutoZone has one, I honestly avoid shopping there. I've used [this kit from Amazon] (https://www.amazon.com/Mityvac-MV8000-Automotive-Test-Bleeding/dp/B00265M9SS/ref=sr_1_1?ie=UTF8&qid=1466703640&sr=8-1&keywords=mity+vac) on multiple cars and it's been great. I've heard a few people mention using a kit they got from Harbor Freight as well.

Can almost guarantee you have air bubbles all throughout the system. Get a mityvac hand bleeder and some fluid and do it again. Master first, then slave.

Mityvac MV8000 Automotive Test and Bleeding Kit https://www.amazon.com/dp/B00265M9SS/ref=cm_sw_r_other_apa_0GCHxbMQ8K6QB

Don't do like I did trying to bleed the slave on a Corrado once... Duct taped the bleed hose to the vac, and apparently the fluid is flammable. Turned the vacuum into a jet engine. :)

So this http://www.amazon.com/gp/aw/d/B00265M9SS/ref=mp_s_a_1_1?qid=1421538722&sr=8-1&pi=AC_SY200_QL40&dpPl=1&dpID=41RZUDpXidL&ref=plSrch
Along with the filter you posted would be fine? This looks a lot easier for making larger batches.

I just picked up a filtration set yesterday. Haven't put a run through but I figured you might like to have the links together. Funnel, Pump, filters.

Amazon has this cheap-ass bleeder kit for about $40. Paid for itself the day I took it out of the box. Pick up the fluid your bike calls for and spend a few minutes on brake maintenance. Your brakes will thank you with better feel and less sponginess.

I picked up the same Mighty Vac pump at O'Reilly Auto for around $40.

http://www.amazon.com/Mityvac-MV8000-Automotive-Brake-Bleeding/dp/B00265M9SS/ref=sr_1_2?ie=UTF8&qid=1319779744&sr=8-2

It takes like 5 minutes with my mityvac. You can do it by pumping the brakes.
A mityvac is only $30.