Do I need these services?

All except the Fuel Injection Service....just make sure you fill up your tank with "Top Tier" gasoline and that'll keep them cleaned out for you.

I would ask about the cost of the spark plug replacement....sounds more like a $150-200 job than $301...I'd remind them it's a 4-cylinder and easy peasy!!

BTW, that's an excellent price for the transmission service....last I checked, my dealer charges $310 for it.

 

I won't comment on the timing, but just considering each item:

Brake Flush $179 <Toyota USA says nothing regarding brake fluid change (presumably what they're actually doing), but Toyota Canada recommends tri-yearly or 48k kms, whichever comes first
Fuel Injection Service $259 <Pure waste of money
Transmission Flush $264 <Toyota USA (and Canada) say nothing regarding transasxle fluid change (presumably what they're actually doing). That said, I would do at least one. Still, that price is ridiculous, even in Canadian dollars it's ridiculous. A trasnsaxle fluid change is no more complex than an oil change, and considering there's no oil filter, the difference in supplies is trivial. I wouldn't pay over $100 USD. Make sure they're using Toyota ATF WS, from freshly opended bottles.
Coolant Flush $235 <Presumably engine coolant change. That's about the usual full-retail price I guess. See the attached schedule to determine if it's warranted.
Inverter Coolant $199 <Per previous comment. Heady thought: how about $200 even

Attached is a summary of the Toyota USA maintenance schedule, extrapolated to 240k miles and 24 years.

 

IMHO:
Spark Plug Replacement $301; Due for replacement
Brake Flush $179; No official Toyota recommendations, but other OEM specify 3-5 years. It's pretty humid in Portland. There is a couple of test you can run.

Fuel Injection Service $259; Hard Pass - buy some over the counter injector cleaner and dump it in on your next fill-up.

Transmission Flush $264, No official Toyota recommendations, but after 14 years and 115K miles, you should probably change it.

Coolant Flush $235
Inverter Coolant $199; Both coolants should probably be changed, You've reached the 10 year time interval but not the mileage interval - chemicals and oils breaks-down and get contaminated over time. If you look at the footnotes of your manual, after the first coolant change; it reverts to 50K mile intervals.

I also have an issue with terminology - a change vs a system flush are very different procedures. One will require at least 2.5x more fluids to accomplish. I know some people don't see a difference, but billing for a flush when they are actually doing a change is, technically FRAUD. The OEM manual ONLY ask that the fluids be CHANGED; doesn't state "flush" in the documentation. Service writers will always try to sell you the expensive option; unless you correct them. That's been my experience.

Here's a web site to get a rough price comparison. I'd ask for a service discount; if they are going to do multiple services in one visit - They're not going away and coming back, so that's saving them time and money; which should reduce your cost. Toyota Prius Spark Plug Replacement Costs

 

One additional comment, some places like to do "flushes" instead of a drain and fill. Save your money, request drain and fill....transmission and coolant doesn't need flushing and, if done wrong, can actually create problems.

 

A lot times the dealerships say flush, when in fact it's a drain and fill. Virtually always.

@Godawgs the elephant in the room: it's your car. Study the schedule (table format I posted early in infinitely easier than trying to make sense of the event-by-event format in Toyota USA's Warranty and Maintenance Booklet), make a decision as to what you're hiring them to do, get a quote.