How can I install Microsoft Flight Simulator 98 on Vista OS?

Install the two patches from here:
http://www.simviation.com/fs98utilities_ess.htm
and try running in Compatibility mode for Win98SE
 
This is going to be a stretch though!

Does the installation stop, or does it allow you to continue after that error message? If it allows you to continue, it may work, since when you start FS it will find a recent DirectX already installed. I think I have seen this with some AutoCAD installations, looking for various Adobe versions etc.

If you are adventurous, you could try this: before you install FS, search the Win7 registry for the section that contains the version of DirectX and either edit it to show DirectX 5 (temporarily)  or add another section which does show DirectX 5 installed. The FS instal routine should then run to completion.If you have a older installation of FS on a Vista OS, you might be able to find the location of those entries.

masqueraid--Thanks.  Does not work because both downloads assumes, & looks for a installed FS.
           I cannot install because it cannot see DirectX in Vista.  I tried to update a DirectX from Microsoft. Was told that I had toe latest Ver.

rh5757- Thanks.  Installation does not go forward at all.  Message says I must install DirectX 5.0 or higher first.  Than closes installation pgm.  (Im using FS CD).

rh5757-  I do not know how to deal with the registry.

I know you don't want to hear this, but maybe it is time to upgrade to a later version of FS which is more aware of the later versions of DirectX? And has more bells and whistles?

I don't have a Win7 system running to feel confident walking you through the registry edits, unfortunately.

Another idea is to run a vitrual machine inside your Vista OS, and have Windows 98SE running in that virtual machine. The "out of the box" Win98SE probably has a version of DirectX closer to v5. Running the virtual machine will reduce your system resources available to the game, but you can skew your memory etc towards the game whenever you do choose to run it. At the extreme, you could set up a dual boot system: both Vista and Win98SE on different partitions on your computer. All this assumes you have access to Windows 98SE. MS Virtual PC is free.

Looking at this objectively there really is no easy way of solving FS98 into Vista.
There isn't a "registry hack" which will fool the game installer into thinking DirectX 10 is DirectX 5.

Also VirtualPC is a non starter as it won't support use of a joystick - rather a serious limitation in a flight sim!

Simplest solution is going to be FS2004 which is the oldest version of FS that Vista will allow to run.

If you are feeling adventurous you could install a separate Win98SE (or even XP) OS and install FS98 to it. This would rely on your PC supporting the alternative OS.
Dual booting XP/Vista isn't a big deal but Win98SE/Vista is hard work.
The best approach would either be a physical switch of hard drives (provided your PC supported E-IDE drives) or if your PC supports "boot from USB" it is possible to create an external drive with Win98SE on that you can simply plug into a USB port when you want to play. There's a hit on performance but as FS98 isn't as resource hungry as its later siblings you shouldn't notice this much on the faster machine (provided you can get USB 2.0 out of it).

However by this stage what is happening is you are making a workaround despite Microsoft's limitations - it would be quicker and simpler to buy FS2004 or even FSX.

Thank you both, Thank You, Thank You. Buying a Microsoft pgm, giving them your money, & than yrs later because of a Microsoft OS, their pgm does not work, is akin to theft.  The next time my computer goes, I will think twice about getting another Microsoft product.  When you buy a book & it becomes old, can you still read it or not?