As an absolute beginner to both music reading and playing, I have a question that will no doubt appear silly, but it is driving me insane. In the key of F there is a Bflat, does this mean that if you have to play the Gmajor chord (GBD) the B will be played as flat, i.e. G Bflat D?
Using your example in the key of F major, chords (triads in this case) are made using notes from that scale. 1-3-5 will make Fmaj., 2-4-6 will make Gmin., as the 4 is Bb, as in the key signature. 3-5-7 will make Amin., 4-6-8 makes Bb maj, same reason as the 2nd chord. 5-7-9 shows as Cmaj.; the relative minor of F (Dmin) will be made from 6-8-10, and 7-9-11 gives a strange sounding chord, Emb5, which just happens to be the top 3 notes of F's dominant chord, called C7.
If you wanted to use a Gmaj. chord in your music, there are no rules saying 'don't', but it would have to include a B natural, shown in music with a natural sign (♮). Lots of songs in F maj. throw a G maj. chord in, instead or as well as a G min., so it's no big deal.
I feel sure this or a similar question has been answered on this site already.
Well you "don't have to", you can play anything you want. There is a thousand formulas were you could actually use a chromatic or borrowed note or chord and it would make sense.
If you mean "I want to keep my harmony and melody in F major strictly" or you are talking about a sheet paper that indicates that (and then forces you to interpret it that way), then yes, you must use Bb anywhere, that is, modify all the chords from the C (major/Ionian) logic:
So in the key of F major, you specially use G-Bb-D (Gminor chord), Bb-D-F (Bb major), E-G-Bb (Eº) and C-E-G-Bb (C7 instead of Cmaj7 when doing a 4-voiced chord), and of course you have to modify other sus2, sus4, 6, and so on that used B. You can see that playing on a piano, if you are on F major, you are playing one black key (Bb) instead of B. Does not matter what basic chord you play, you have to substitute it.
Anyway your question is not well-formulated. If you play a Bb instead of a B in a G chord, then you are not playing a G chord anymore, but a Gm chord. So playing in F major implies using a minor G chord as a reference.