Hi, the easy way to check if your 98 A4 can use the remote flick key (which it should) is to check the part number on your central locking pump, which is located in the boot, on the drivers side, under the little side tray just into the rear wing (it is inside a foam shell).
If the suffix on your pump is greater than 'A' (which did not have radio reciever) you will be able to use remote flick keys.
As your car is on a 98, i am pretty sure that it requires a 2 button remote, and not the three button.
Then you need to either take all your keys to Audi and have the transponders swapped, or as i did, canibalise my second main key and swap the transponder capsule from your old style key to your new flip key. (you can also use the blade if you dont want the expense of getting another cut, but it requires reshaping with a small file to match a flip key blade).
Then sync your remote to your car and away you go.
I did this on my 97 A4 TDI SE, which had the same style key as yours. I had to replace my central locking pump with a radio version, any suffix will do, i used an A3 'G' suffix pump on mine (if you change to a pump with another suffix you will need to use VAG-COM to change the soft coding, or the alarm etc wont work).
It is probably easier to buy a 'Remote locking' addon though, + the range on the audi remotes is terrible.
