Will bootloader unlocking provide access to all the apps in the Play Store? My flyer doesn't allow few apps to be installed from the Play Store as it shows "This app is not compatible with your device" and this incompatibility is not due to OS. If I get the apk of this app from a forum, I can install it but few apps don't have apks outside Play Store.

I don't want to root my device, but simply unlock the bootloader so that I can access all of the apps on the Play Store without country/device restrictions. I read somewhere that it is mandatory to flash the device while unlocking the bootloader.

If I unlock the bootloader of my Flyer will I be able to install all OS compatible apps from the Play Store?
No. Unlocking the bootloader will do nothing for Google Play. Even rooting won't do anything by itself as far as phone compatibility goes.

To get access to the apps without device restrictions, you must have a rooted phone. You then must edit the build.prop file to change your phone model to one that can install the app in question. See this android.se question.

To get access to the apps without country restrictions, no root is needed. You must instead have a proxy whos IP address is inside the particular country desired (generally the U.S.). Or you could create an account via a U.S. proxy on your desktop, then push the apps to your linked device despite it's out-of-country location (see this explanation). Alternatively, you could have a rooted phone and download Market Enabler.