Do the flags look sharp on the file you are sendng to the printer? If so, then you should talk to your printer and ask them why the proof looks bad. Sometimes PDF proofs will be optimized at a lower resolution in order to reduce the file size to allow it to be emailed. Are you zooming in on your proof? that proof is showing you what the printed piece will look like, (It's unlikely someone will be using a magnifying glass on your printed piece). Did you place the images into Illustrator and save as a PDF (recommended), or copy and paste? You might get slightly better results if you re-size the tif files in Photoshop, then place them in your Illustrator file at the correct size. Also, if your original files are RGB, the printer has probably converted them to CMYK, which your PDF proof will show (Acrobat> Tools> output Preview> Show> RGB).
I dragged those flags from image folder directly into illustrator, then save as .ps file > then convert into normal pdf file.
The PDF I sent to the printer seems fine on everything and equally same size as the one from printer. The printer's version is kind of "pixelated blur " on the flag and not blur as of size matter.
I use the same method to create files with flags for printing and never had this kind of problem. What I'll do now is saving all the flags in CMYK JPG and send to the printer again to see if it's ok.
Best practice would be to link your images to your Illustrator file (File> Place). I'm not sure if drag and drop works exactly the same. What version of Illustrator are you using? Do you have Photoshop? Saving as .ps and distilling to PDF is an old work flow, just save as PDF. I would still ask the printer about the original PDF proof, it's possible nothing is wrong (except the proof they sent you).