Combine FFT's of shorter length than sample data to get spectrum of all data I have a set of sample data, a logarithmic swept sine as it happens, that is 1 second in duration sampled at 100kHz giving 100k samples. I want to calculate the frequency spectrum of the complete data however the FFT library function available only supports 4096 samples maximum. 

Is it valid to sequentially FFT 4096 samples and sum the resulting data. Thereby ending up with 4096/2 frequency points that show the frequency content of the entire 100k samples?

I guess it is necessary to window each block of 4096 samples to be FFT'd but this would mean that the portions of the frequency content would be reduce in amplitude artificially. 

How does one handle the phase information?
Yes you can do it, but you will loose spectral resolution. The method you mention is a variant of the Welch's spectogram estimation algorithm which relies on the block based estimation of power spectrum of a long sequence in terms of shorter blocks within it. 

Given that you have a data of $100$k in length which was sampled at $F_s = 100$k, then a full length DFT after rectangular windowing would provide you a spectral resolution of about $1$ Hz to $3$ Hz, where as a window of $4096$ samples would yield about $25$ Hz to $75$ Hz of spectral resolution.

If this resolution is enough for your purposes, then you can (and indeed you should better) perform the block based averaged spectral analysis in order to trade-off between the reduced spectral resolution and an increased estimation accuracy (decreased estimation variance)