The flu shot is a recommended vaccine for kids and adults. And it's on a shortlist of vaccines Consumer Reports recommends adults should be getting:
Flu
Pneumonia
Tdap
Measles
Shingles
Shingles. Everyone 50 and older should get the shingles vaccine and specifically Shingrix. If you've had a vaccine called Zostavax, you should still get Shingrix. It's more effective. The Shingrix vaccine is 97% effective at preventing shingles in folks 50 to 69 years old and then 91% after that.
The Shingrix vaccine is in short supply--- so you may need to be put on a waitlist.
Here is a summarization of the Consumer Reports article:
Pneumonia vaccine. All adults should get the vaccine known as PPSV23 (Pneumovax 23) once they turn 65
Tdap vaccine. Older adults need a single dose of Tdap for if they’ve never had one before. (a dose of Tdap has been recommended for all adults since 2005, but only about 20 percent of older adults have ever received it, according to the cdc.) People 19 and older should get a booster of either Tdap or TD every 10 years
Measles booster. Anyone born in or after 1957 who doesn’t have documented evidence of immunity to measles should get a dose of MMR.